+
    ,i<                       R t ^ RIt^ RIt^ RIt^ RIt^ RIHt ^ RIHt ^ RI	H
u Ht ^ RIt^ RIt^ RIHtHtHtHtHtHtHtHtHt ^ RIt^ RIHt ^ RIHtHtHtHt ^ RIt ^ RI!H"t" ^ RI#H"u H$t$ ^ RI%H"u H&t' ^ RI(H)t) ^ RI*H+t+ ^ R	I,H-t- ^ R
I.H/t/ ^RI0H1t1 ^ RI2H3t3H4t4H5t5H6t6H7t7H8t8 ^ RI9H:t:H;t;H<t<H=t=H>t>H?t?H@t@ ^ RIAHBtB ^ RICHDtD ^ RIEHFtFHGtGHHtHHItIHJtJHKtKHLtLHMtMHNtN ^ RIOHPtPHQtQ ^ RIRHSu HTtU ]".tV]P                  P                  tX ]! . RO]Y4      tZ]! . RO]Y4      t[]! . RO]Y4      t\]! . RO]Y4      t]]! . RO]Y4      t^]! . RO]Y4      t_]! . RO]Y4      t` ! R R4      ta ! R R4      tb]N! ]"P                  4       ! R R4      4       td ! R R4      te ! R R4      tf ! R R4      tgR  thR! tiR" tj]P                  P                  R# 4       tl ! R$ R%4      tmR& tnR' toR( tpR) tq ! R* R+4      tr ! R, R-4      tsR. ttR/ tuR0 tv ! R1 R24      tw ! R3 R44      tx]N! ]"P                  4       ! R5 R64      4       tz]N! ]"P                  4       ! R7 R84      4       t|]N! ]"P                  4       ! R9 R:4      4       t~]N! ]"P                  4       ! R; R<4      4       t ! R= R>4      tR? t ! R@ RA4      t]N! ]"EP                  4       ! RB RC4      4       t ! RD RE4      t]N! ]"EP                  4       ! RF RG]4      4       t]N! ]"EP                  4       ! RH RI]4      4       t]EP                  EP                  RJ 4       t]N! ]"EP                  4       ! RK RL4      4       t ! RM RN4      t]! RO. RQO4      t]! . ROR^ R^^^] EP$                  ! R4      ,          ^] EP$                  ! R4      ,          ,           ,          ^^] EP$                  ! R4      ,          ^] EP$                  ! R4      ,          ,           ,          RRQ7      ]! . RO. RO^ R^^^] EP$                  ! R4      ,          ^] EP$                  ! R4      ,          ,           ^] EP$                  ! R4      ,          ,           ,          ^^] EP$                  ! R4      ,          ^] EP$                  ! R4      ,          ,           ^] EP$                  ! R4      ,          ,           ,          RRQ7      ]! . RO^^ R^^^] EP$                  ! R4      ,          ^] EP$                  ! R4      ,          ,           ,          ^^] EP$                  ! R4      ,          ^] EP$                  ! R4      ,          ,           ,          RRQ7      ]! . RO. RO^ ^ ^ ^ ^ ^ RQ7      .t]! . R^ ^ ^ ^ ^ ^ RQ7      ]! ] P8                  ! . . . .4      EP(                  R^ ^ . RO. RO. RO. RORQ7      ]! ] P8                  ! . . . .4      R^ ^ . . . . RQ7      .t]N! ]"EP,                  4       ! RR RS4      4       t]N! ]"EP0                  4       ! RT RU4      4       tRV t ! RW RX4      t ! RY RZ4      t ! R[ R\4      tR] tR^ tR_ t]P                  EPC                  R`] EPD                  ! R4      R3] EPD                  ! R4      R3.4      Ra 4       tRb t]P                  EPC                  Rc. RO4      Rd 4       t]P                  EPC                  Re]"EP                  ] P:                  ! ^
4      ^ 33]"EPL                  ] P:                  ! ^
4      ] P:                  ! ^
4      33.4      Rf 4       tRRgR/Rh llt]N! ]"EPR                  ]"EPT                  4      Ri 4       tRj tRk t]P                  EP]                  Rl4       ! Rm Rn4      4       t]P                  EP]                  Rl4       ! Ro Rp4      4       t ! Rq Rr4      t]N! ]"EPR                  4       ! Rs Rt4      4       tRu t]N! ]"EPR                  4       ! Rv Rw4      4       t]N! ]"EPT                  4       ! Rx Ry4      4       t]P                  P                  RzR{R|7      ]P                  EP]                  R}4      R~ 4       4       tR t]P                  EPp                  ]P                  EP]                  R4      ]P                  EP]                  R4      ]N! ]"EP                  4      R 4       4       4       4       t]X! RzRR7      R 4       t]N! ]"EP                  4      ]P                  P                  RRR7      R 4       4       t]N! ]"EPx                  4       ! R R4      4       t ! R R4      t]N! ]"EP~                  4       ! R R]4      4       t]N! ]"EP                  4       ! R R]4      4       t]N! ]"EP                  4       ! R R]4      4       t ! R R4      t]N! ]"EP                  4       ! R R4      4       t ! R R4      tR tR tRPRRRRRRR/R ltR tR tR t]N! ]"EP                  4       ! R R4      4       t]N! ]"EP                  4       ! R R4      4       t]N! ]"EP                  4       ! R R4      4       t]N! ]"EP                  4       ! R R4      4       tR tR tR t ! R R4      t ! R R4      t ! R R4      t ! R R4      t ! R R4      t]N! ]"EP                  4       ! R R4      4       t ! R R4      t ! R R4      t ! R R4      t ! R R4      t ! R R4      t ! R R4      t ! R R4      t] EP                  EP                  R4      t]EP                  ^
4      t]EP                  ^
4      t]P                  EPC                  R]"EP                  ]33]"EP                  ]]"EP                  EP                  33]"EP                  ]]33]"EP                  ]]33.4      R 4       t ! R R4      t ! R R4      t ! R R4      t ! R R4      tR t]X! RRR7      R 4       tR# )zTest functions for stats module

WRITTEN BY LOUIS LUANGKESORN <lluang@yahoo.com> FOR THE STATS MODULE
BASED ON WILKINSON'S STATISTICS QUIZ
https://www.stanford.edu/~clint/bench/wilk.txt

Additional tests by a host of SciPy developers.
N)
namedtuple)product)	assert_assert_equalassert_almost_equalassert_array_almost_equalassert_array_equalassert_approx_equalassert_allclosesuppress_warningsassert_array_less)raises)arrayarangefloat32power)kolmogn)FuncData)binom)optimize)check_named_results)_broadcast_concatenateSmallSampleWarningtoo_small_nd_omittoo_small_nd_not_omittoo_small_1d_omittoo_small_1d_not_omit)_permutation_distribution_t_chk_asarray_momentLinregressResult_xp_mean_xp_var_SimpleChi2)	AxisError)skip_xp_invalid_arg)	array_namespaceeager_warnsis_lazy_arrayis_numpyis_torchxp_default_dtypexp_sizeSCIPY_ARRAY_APImake_xp_test_case)xp_assert_closexp_assert_equal      ?      ?c                     a  ] tR t^Ot o ]P
                  ! ]P                  4      P                  t]	! ]
P                  4      R 4       t]	! ]
P                  4      ]P                  P!                  R4      R 4       4       t]	! ]
P$                  4      R 4       t]	! ]
P(                  4      R 4       t]! RRR7      R	 4       t]	! ]
P0                  4      R
 4       t]! RRR7      R 4       t]	! ]
P(                  ]
P0                  4      R 4       t]! RRR7      ]	! ]
P(                  ]
P0                  4      R 4       4       t]	! ]
P:                  4      R 4       tRtV t R# )TestTrimmedStatsc           	        \        V4      pVP                  \        VR 7      p\        P                  ! VRR4      p\        WAP                  R4      4       \        P                  ! VRRR7      p\        P                  ! VRR7      p\        WV4       VP                  VP                  R4      R4      p\        P                  ! VRR7      p\        WAP                  V4      4       \        P                  ! V^ R7      p\        WAP                  V^ R7      4       \        P                  ! V^R7      p\        WAP                  V^R7      4       \        P                  ! VRRR7      p\        WAP                  R	4      4       \        P                  ! VR^ R7      p. ROp\        WAP                  V4      4       \        P                  ! VRR^ R
7      p. ROp\        WAP                  V4      4       \        P                  ! V4      RRR13,          P                  VP                  RR7      p	\        P                  ! V	R^ R7      p^RRRVP                  VP                  VP                  .p\        WAP                  V4      4       \        P                  ! VR^R7      p^^
^^VP                  VP                  VP                  VP                  VP                  .	p\        WAP                  V4      4       \        P                  ! VRR^R
7      pR^
^^VP                  VP                  VP                  VP                  VP                  .	p\        WAP                  V4      4       R# )dtypeT      @limits	inclusiveNr:        O@axis)r:   r?   g     ?@)r:   r;   r?   )copy      @      @      @      TT)FF	      )rE   =   )rE      )         '@rI   
            TF)      %@rN   rI   rO   rP   rQ   rR   )   rR   FT)r+   asarrayXstatstmeanr/   reshaper   meanxpxatsetnan)
selfxpdefault_dtypexyy1y2x_2dy_truex_2d_with_nans
   &&        >/usr/lib/python3/dist-packages/scipy/stats/tests/test_stats.py
test_tmeanTestTrimmedStats.test_tmeanS   ss   (,JJqJ.KK6<0::c?+[[6^D[[4(zz"))C.&1KK4(774=)KK1%774a701KK1%774a701KKW48::d+,KKW15.::f-.KKWAN0::f-.tRW-11"&&t1DKKgA>S#sBFFBFFBFF;::f-.KKW15RRH::f-.KKW"/a9r2r266266266266266J::f-.    z>ignore:invalid value encountered in divide:RuntimeWarning:daskc                   VP                  \        P                  4       4      p\        P                  ! VRRR7      p\        W1P                  R4      4       \        P                  ! VRR7      p\        W1P                  V^R7      4       VP                  VP                  R4      R4      p\        P                  ! VRR7      p\        W1P                  V^R7      4       \        P                  ! V^ R7      p\        W1P                  RR4      4       \        P                  ! V^R7      p\        W1P                  RR	4      4       \        P                  ! VR^RR
7      p\        V^ ,          VP                  R4      4       \        P                  ! VR^RR
7      p\        V^ ,          VP                  R4      4       \        V^,          VP                  VP                  4      4       R# )rE   r9   g@Nr<   
correctionr=   r>   g     v@g㪪@)r:   r?   r;         @g@rD   rG   rH   rJ   )rI   rW             )rY   rZ   tolistr[   tvarr/   varr]   r   fullr0   rb   )rc   rd   rf   rg   rj   s   &&   rm   	test_tvarTestTrimmedStats.test_tvar   sY   
 JJqxxz"JJq<@::&89:JJq&66!623zz"))C.&1JJt$'66$1656JJt!$774/0JJt!$77445 JJtFlK!bjjo. JJtFlK!bjj):;<!bjj01rp   c                   VP                  \        P                  4       4      p\        P                  ! VRR4      p\        W1P                  R4      4       \        P                  ! VRR7      p\        W1P                  V^R7      4       R# )rE   gBĆ/H@Nr<   rr   rD   rG   )rY   rZ   r{   r[   tstdr/   stdrc   rd   rf   rg   s   &&  rm   	test_tstdTestTrimmedStats.test_tstd   s_    JJqxxz"JJq&,/::&89:JJq&66!623rp   c           	     \   VP                  R 4      p\        \        P                  ! V4      VP	                  R4      4       \        \        P                  ! V^ R7      VP	                  R4      4       \        \        P                  ! V^ RR7      VP	                  R4      4       VP                  VR
4      p\        \        P                  ! V^ RR7      VP	                  RR.4      4       \        \        P                  ! V^R7      VP	                  . RO4      4       \        \        P                  ! VRR7      VP	                  R4      4       \        P                  ! VP                  R 4      ^	4      P                  VP                  4      p\        \        P                  ! V4      VP	                  VP                  4      4       VP                  VP                  ^4      R4      p\        P                  ! V^^R	7      p\        W1P	                  \        P                  ^^^.4      4       R# )      $@        
lowerlimitF)r   r;         ?       @r>   N)r   r?   rw   rE   )r   r         @      @       @   r   )r   r0   r[   tminrY   r]   r_   r`   ra   rb   nprc   rd   rf   ress   &&  rm   	test_tminTestTrimmedStats.test_tmin   si   IIcN

1rzz"~6

13RZZ^D

1eDbjjQSnUJJq&!

1eD

B8,	.

11-rzz:N/OP

140"**R.AFF299S>1%))"&&1

1rzz"&&'9: JJryy}f-jjqq1ZZAr(:;<rp   Tz4Only NumPy arrays support scalar input/`nan_policy`.np_onlyreasonc           	        \        \        P                  ! ^4      ^4       \        P                  ! R4      p\        P
                  V^	&   \        4       ;_uu_ 4       pVP                  \        R4       \        \        P                  ! VRR7      R4       Rp\        \        VR7      ;_uu_ 4        \        P                  ! VRR7       R	R	R	4       R
p\        \        VR7      ;_uu_ 4        \        P                  ! VRR7       R	R	R	4       R	R	R	4       R	#   + '       g   i     LV; i  + '       g   i     L-; i  + '       g   i     R	# ; i)r   r   invalid value*omit
nan_policyr   The input contains nan valuesmatchraiseNnan_policy must be one of...foobar)r   r[   r   r   r   rb   r   recordRuntimeWarningassert_raises
ValueErrorrc   rd   rf   supmsgs   &&   rm   test_tmin_scalar_and_nanpolicy/TestTrimmedStats.test_tmin_scalar_and_nanpolicy        	UZZ]A&IIcNvv!  CJJ~'78A&92>1Cz55

11 60Cz55

12 6 !  65 65 !  =   AD=0D		#D=,D*	D=D'"D=*D:5D==E	c                   VP                  R 4      p\        \        P                  ! V4      VP	                  R4      4       \        \        P                  ! V^	R7      VP	                  R4      4       \        \        P                  ! V^	RR7      VP	                  R4      4       VP                  VR4      p\        \        P                  ! V^	RR7      VP	                  RR.4      4       \        \        P                  ! V^R7      VP	                  . RO4      4       \        \        P                  ! VRR7      VP	                  R4      4       \        P                  ! VP                  R 4      ^	4      P                  VP                  4      p\        \        P                  ! V4      VP	                  VP                  4      4       \        4       ;_uu_ 4       pVP                  \        R	4       VP                  VP                  ^4      R4      p\        P                  ! V^^R
7      p\        WAP	                  ^^^\        P                  .4      4       RRR4       R#   + '       g   i     R# ; i)r         "@
upperlimitF)r   r;   r         @r>   NzAll-NaN slice encountered)r   r?   r   )r         @r8   r   r   r   )r   r0   r[   tmaxrY   r]   r_   r`   ra   rb   r   filterr   r   )rc   rd   rf   r   r   s   &&   rm   	test_tmaxTestTrimmedStats.test_tmax   s   IIcN

1rzz"~6

13RZZ^D

1eDbjjQSnUJJq&!

1eD

B8,	.

11-rzz:N/OP

140"**R.AFF299S>1%))"&&1

1rzz"&&'9:   CJJ~'BC

299R=&1A**Q2A6CCQ2rvv,>!?@	 !   s   A=II0	c           	        \        \        P                  ! ^4      ^4       \        P                  ! R4      p\        P
                  V^&   \        4       ;_uu_ 4       pVP                  \        R4       \        \        P                  ! VRR7      R4       Rp\        \        VR7      ;_uu_ 4        \        P                  ! VRR7       R	R	R	4       R
p\        \        VR7      ;_uu_ 4        \        P                  ! VRR7       R	R	R	4       R	R	R	4       R	#   + '       g   i     LV; i  + '       g   i     L-; i  + '       g   i     R	# ; i)r   r   r   r   r   r   r   r   r   Nr   r   )r   r[   r   r   r   rb   r   r   r   r   r   r   s   &&   rm   test_tmax_scalar_and_nanpolicy/TestTrimmedStats.test_tmax_scalar_and_nanpolicy   r   r   c                   VP                  VP                  ^
VP                  R7      R4      P                  p\	        V4      '       d   \        V4      MVP                  p\        \        P                  ! V4      VP                  ^ ^.VR7      4       \        \        P                  ! V4      VP                  ^^	.VR7      4       \        \        P                  ! V^R7      VP                  VP                  R.4      4       \        \        P                  ! V^R7      VP                  RVP                  .4      4       R# )rO   r6   r   r   r   r   NrE   rw   )r]   r   int16Tr(   r+   r7   r0   r[   r   rY   r   rb   )rc   rd   rf   expect_dtypes   &&  rm   test_tmin_tmax_int_dtype)TestTrimmedStats.test_tmin_tmax_int_dtype   s    JJryy288y4f=??
 0=Q/?/?'+QWW

1rzz1a&z'MN

1rzz1a&z'MN 	

13RZZ5MN

13RZZRVV5MNrp   z%Only with data-dependent output dtype
eager_onlyr   c                    VP                  RR4      p\        \        P                  ! VR,          4      V4       \        \        P                  ! VR,          4      V4       R# )rE   Nl            l   
        )NNNN)r   r0   r[   r   r   rc   rd   rf   s   && rm   test_gh_22626TestTrimmedStats.test_gh_22626  sB     IIeX&

1W:.2

1W:.2rp   c                ~   VP                  \        P                  4       4      p\        P                  ! VRRR7      pVP                  . RO4      p\        W1P                  V^R7      \        V4      R,          ,          4       \        \        P                  ! VR	^
.R7      \        P                  ! VRR7      4       R# )
   r9   rr   r1   r<   N)r   rF   rX   )r   r8   r   r   r   rU   )rY   rZ   r{   r[   tsemr/   r   r,   )rc   rd   rf   rg   y_refs   &&   rm   	test_tsemTestTrimmedStats.test_tsem  s~    JJqxxz"JJq=A

/066%A669LLM

1b"X6

1T8RSrp    N)!__name__
__module____qualname____firstlineno__r   finfofloat64	precisiondprecr.   r[   r\   rn   r|   pytestmarkfilterwarningsr   r   r   r   r   skip_xp_backendsr   r   r   r   r   r   r   r   __static_attributes____classdictcell____classdict__s   @rm   r4   r4   O   s    HHRZZ **Eu{{#,/ $,/\ uzz"[[H2 #28 uzz"4 #4 uzz"= #=* dSU3U3 uzz"A #A. dSU3U3 uzz5::.O /O .UVuzz5::.3 / W3 uzz"T #Trp   r4   c                      a  ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tR tR tR tR tR tR tR tR tR tR tR tR tRtV tR# )TestPearsonrWilkinsoni     W.II.D. Compute a correlation matrix on all the variables.

All the correlations, except for ZERO and MISS, should be exactly 1.
ZERO and MISS should have undefined or missing correlations with the
other variables.  The same should go for SPEARMAN correlations, if
your program has them.
c                n    \         P                  ! \        \        4      pV^ ,          p\        VR4       R# ry   r   N)r[   pearsonrrZ   r	   rc   rg   rs   &  rm   test_pXXTestPearsonrWilkinson.test_pXX&  s%    NN1QaDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   r   rZ   BIGr	   r   s   &  rm   
test_pXBIG TestPearsonrWilkinson.test_pXBIG+  s%    NN1S!aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   r   rZ   LITTLEr	   r   s   &  rm   test_pXLITTLE#TestPearsonrWilkinson.test_pXLITTLE0  s%    NN1V$aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   r   rZ   HUGEr	   r   s   &  rm   test_pXHUGE!TestPearsonrWilkinson.test_pXHUGE5  %    NN1T"aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   r   rZ   TINYr	   r   s   &  rm   test_pXTINY!TestPearsonrWilkinson.test_pXTINY:  r   rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   r   rZ   ROUNDr	   r   s   &  rm   test_pXROUND"TestPearsonrWilkinson.test_pXROUND?  s%    NN1U#aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\        VR4       R# r   )r[   r   r   r	   r   s   &  rm   test_pBIGBIG"TestPearsonrWilkinson.test_pBIGBIGD  s%    NN3s#aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   r   r   r   r	   r   s   &  rm   test_pBIGLITTLE%TestPearsonrWilkinson.test_pBIGLITTLEI  s%    NN3v&aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   r   r   r   r	   r   s   &  rm   test_pBIGHUGE#TestPearsonrWilkinson.test_pBIGHUGEN  %    NN3t$aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   r   r   r   r	   r   s   &  rm   test_pBIGTINY#TestPearsonrWilkinson.test_pBIGTINYS  r  rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   r   r   r  r	   r   s   &  rm   test_pBIGROUND$TestPearsonrWilkinson.test_pBIGROUNDX  s%    NN3u%aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\        VR4       R# r   )r[   r   r   r	   r   s   &  rm   test_pLITTLELITTLE(TestPearsonrWilkinson.test_pLITTLELITTLE]  s%    NN6&)aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   r   r   r   r	   r   s   &  rm   test_pLITTLEHUGE&TestPearsonrWilkinson.test_pLITTLEHUGEb  %    NN6$'aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   r   r   r   r	   r   s   &  rm   test_pLITTLETINY&TestPearsonrWilkinson.test_pLITTLETINYg  r  rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   r   r   r  r	   r   s   &  rm   test_pLITTLEROUND'TestPearsonrWilkinson.test_pLITTLEROUNDl  s%    NN6%(aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\        VR4       R# r   )r[   r   r   r	   r   s   &  rm   test_pHUGEHUGE$TestPearsonrWilkinson.test_pHUGEHUGEq  %    NN4%aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   r   r   r   r	   r   s   &  rm   test_pHUGETINY$TestPearsonrWilkinson.test_pHUGETINYv  r$  rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   r   r   r  r	   r   s   &  rm   test_pHUGEROUND%TestPearsonrWilkinson.test_pHUGEROUND{  %    NN4&aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\        VR4       R# r   )r[   r   r   r	   r   s   &  rm   test_pTINYTINY$TestPearsonrWilkinson.test_pTINYTINY  r$  rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   r   r   r  r	   r   s   &  rm   test_pTINYROUND%TestPearsonrWilkinson.test_pTINYROUND  r+  rp   c                n    \         P                  ! \        \        4      pV^ ,          p\        VR4       R# r   )r[   r   r  r	   r   s   &  rm   test_pROUNDROUND&TestPearsonrWilkinson.test_pROUNDROUND  s%    NN5'aDAc"rp   r   N)r   r   r   r   __doc__r   r   r   r   r   r  r  r  r  r  r  r  r  r  r  r"  r&  r)  r-  r0  r3  r   r   r   s   @rm   r   r     sx     #
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
# #rp   r   c                     a  ] tR tRt o R tR tR tR tR t]	P                  P                  RRR	.4      R
 4       tR tR tR tR tR t]	P                  P%                  R4      R 4       t]! RR7      ]	P                  P                  R. R'O4      R 4       4       tR tR tR t]	P                  P3                  ^
4      ]	P                  P5                  R4      ]	P                  P                  RR(4      ]	P                  P                  RR)4      R 4       4       4       4       t]	P                  P8                  ]	P                  P                  RR(4      R 4       4       t]	P                  P                  R^ ^.4      R 4       tR  tR! t ]	P                  P%                  R4      R" 4       t!R# t"]	P                  P                  R. R*O4      ]	P                  P                  R. R(O4      R% 4       4       t#R&t$V t%R$# )+TestPearsonr  c                    \         P                  ! \        \        4      pRp\        W4       \	        VP
                  VP                  4       R# correlationNr;  pvalue)r[   r   rZ   r   r   r;  	statisticrc   r   
attributess   &  rm   test_pearsonr_result_attributes,TestPearsonr.test_pearsonr_result_attributes  s1    nnQ".
C,S__cmm4rp   c           
     &   VP                  R 4      p\        P                  ! W"4      w  r4\        W1P	                  R4      RR7       \        WAP	                  R4      \
        P                  ! ^\
        P                  ! R4      ,          4      R7       R# )r   r   V瞯<atolr   Nr   r[   r   r/   rY   r   sqrtspacingrc   rd   ar   probs   &&   rm   test_r_almost_exactly_pos1'TestPearsonr.test_r_almost_exactly_pos1  s[    IIcN..&::c?7 	jjoBGGAbjjo<M4NOrp   c           
     (   VP                  R 4      p\        P                  ! W") 4      w  r4\        W1P	                  R4      RR7       \        WAP	                  R4      \
        P                  ! ^\
        P                  ! R4      ,          4      R7       R# )r   r   rD  rE  r   N      rG  rJ  s   &&   rm   test_r_almost_exactly_neg1'TestPearsonr.test_r_almost_exactly_neg1  s^    IIcN..B'::d+%8 	jjoBGGAbjjo<M4NOrp   c                    VP                  . RO4      pVP                  . RO4      p\        P                  ! W#4      w  rE\        WAP                  R4      4       \        WQP                  R4      4       R# )rW   NrU   ry   rW   )ry   ry   r   LXz?UUUUUU?)rY   r[   r   r/   )rc   rd   rK  br   rL  s   &&    rm   
test_basicTestPearsonr.test_basic  sQ     JJz"JJy!..&::h/0jjo.rp   c                   R p\         P                  ! \        P                  VR7      ;_uu_ 4        VP	                  . RO4      pVP	                  . RO4      p\        P
                  ! W44      w  rV\        WQP	                  VP                  4      4       \        WaP	                  VP                  4      4       RRR4       R#   + '       g   i     R# ; i)An input array is constantr   NMbX?r]  r]  rh|?v/?gsh|??r   warnsr[   ConstantInputWarningrY   r   r/   rb   rc   rd   r   rf   rg   r   ps   &&     rm   test_constant_input TestPearsonr.test_constant_input  s     +\\%44C@@

01A

01A>>!'DAAzz"&&12Azz"&&12 A@@@   BCC	r7   r   r   c                   \        \        V4      p\        W4      pVP                  ^^^\        P                  ! ^VR7      ,           .VR7      pVP                  ^^^^\        P                  ! ^VR7      ,          ,           .VR7      pRp\        P
                  ! \        P                  VR7      ;_uu_ 4        \        P                  ! WE4       RRR4       R#   + '       g   i     R# ; i)rE   r6   z/An input array is nearly constant; the computedr   N)	getattrr   rY   rI  r   rb  r[   NearConstantInputWarningr   )rc   rd   r7   npdtyperf   rg   r   s   &&&    rm   test_near_constant_input%TestPearsonr.test_near_constant_input  s    "e$"JJ1a"**Qg">>?uJMJJ1a!BJJq$@"@@AJO?\\%88DD NN1  EDDDs   9CC+	c                J   VP                  . ROVP                  R7      pVP                  . ROVP                  R7      p\        P                  ! W#4      w  rE\	        WAP                  RVP                  R7      4       \	        WQP                  RVP                  R7      4       R# )y)r?r6   ge;E?g3R?N)rp  gxd{s?gnp?g$9"o?ge =:k?)goȟg`
,gzg2l?g>??'rY   r   r[   r   r/   rc   rd   rf   rg   r   re  s   &&    rm   test_very_small_input_values)TestPearsonr.test_very_small_input_values  s     JJVZZ  )JJNZZ  )~~a# 	::&8

:KL::&8

:KLrp   c                b   R VP                  . ROVP                  R7      ,          pR VP                  ^VP                  R7      ,          p\        P                  ! W#4      w  rE\        WAP                  RVP                  R7      4       \        WQP                  RVP                  R7      4       R# )gY)	kRr6   rU  g͗~-?N)ry   ry   ry   rW   rW   rW   rW   )rY   r   r   r[   r   r/   rr  s   &&    rm   test_very_large_input_values)TestPearsonr.test_very_large_input_values  s     1DD1BJJ//~~a# 	::&8

:KL::&:"**:MNrp   c                J   VP                  . ROVP                  R7      pVP                  . ROVP                  R7      p\        P                  ! W#4      w  rE\	        WAP                  RVP                  R7      4       \	        WQP                  RVP                  R7      4       R# )7	ir6   g*D{?gݣ?N)ry  gNig_b4igZbi)gDig<'(½igmQiZbtirq  rr  s   &&    rm   !test_extremely_large_input_values.TestPearsonr.test_extremely_large_input_values  sx     JJ9JLJJ;2::JN~~a# 	::&7rzz:JK::&7rzz:JKrp   c                &   VP                  R R.4      pVP                  RR.4      p\        P                  ! W#4      pVw  rVVP                  R 4      p\        WW4       \        Wg4       VP	                  4       w  r\        W) 4       \        W4       R# )r   r   r   r8   NrY   r[   r   r0   confidence_interval
rc   rd   rf   rg   r   r   re  onelowhighs
   &&        rm   test_length_two_pos1!TestPearsonr.test_length_two_pos1  s|     JJBx JJBx nnQ"jjn++-	T""rp   c                (   VP                  R R.4      pVP                  RR.4      p\        P                  ! W#4      pVw  rVVP                  R4      p\        WW) 4       \        Wg4       VP	                  4       w  r\        W) 4       \        W4       R# )r   r   r   r8   Nr~  r  s
   &&        rm   test_length_two_neg1!TestPearsonr.test_length_two_neg1  s~     JJBx JJBx nnQ"jjn4 ++-	T""rp   *ignore:invalid value encountered in dividec                   R p\         P                  ! \        P                  VR7      ;_uu_ 4        VP	                  RR.4      pVP	                  RR.4      p\        P
                  ! W44      w  rV\        WQP	                  VP                  4      4       \        WaP	                  VP                  4      4       RRR4       R#   + '       g   i     R# ; i)r[  r   r]  r_  r`  Nra  rd  s   &&     rm   test_length_two_constant_input+TestPearsonr.test_length_two_constant_input  s    
 +\\%44C@@

E5>*A

E5>*A>>!'DAAzz"&&12Azz"&&12 A@@@rh  Tr   z$alternative, pval, rlow, rhigh, signc                (   . ROp\         P                  ! . RO4      V,          p\        P                  ! WxVR7      p	\	        V	P
                  RV,          RR7       \	        V	P                  VRR7       V	P                  4       p
\	        WV3RR7       R# )	rW   alternativeg?-q=rtolư>NrW   rE   r   r   )ry   rW   r1   rW   )r   r   r[   r   r
   r>  r=  r  )rc   r  pvalrlowrhighsignrd   rf   rg   resultcis   &&&&&&&    rm   test_basic_exampleTestPearsonr.test_basic_example%  sp     HH^$t++>((*<T*ANt$7'')5M5rp   c                &   VP                  R 4      pV) p\        P                  ! W#RR7      p\        P                  ! W#RR7      p\        VP                  VP                  R4      4       \        VP                  VP                  R4      RR7       R# )	r   greaterr  lessr   r   g#B;rE  N)r   r[   r   r/   r=  rY   )rc   rd   rf   rg   test_greater	test_lesss   &&    rm   (test_negative_correlation_pvalue_gh177955TestPearsonr.test_negative_correlation_pvalue_gh177956  sh    IIcNB~~a	BNN1V<	++RZZ^<	(("**R.uErp   c                <   VP                  . RO4      pVP                  . RO4      p\        P                  ! W#4      pVw  rVVP                  R 4      p\        WW) 4       \        V^ V,          RR7       VP	                  4       w  r\        W) 4       \        W4       R# )r   Hz>rE  Nr   r   r   )r8   g      g      *)rY   r[   r   r/   r  r0   r  s
   &&        rm   #test_length3_r_exactly_negative_one0TestPearsonr.test_length3_r_exactly_negative_one>  s~    JJ|$JJ'nnQ" jjo4 1S5t,++-	T""rp   c                   . ROp^.pRp\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! W4       RRR4       . ROp^^.pRp\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! W4       RRR4       ^.p^.pRp\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! W4       RRR4       . ROp. ROpRp\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! W4       RRR4       Rp\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! ^^.^^.RR	7       RRR4       \        P                  ! ^^.^^.4      p\         P                  ! \        VR7      ;_uu_ 4        VP                  R
R	7       RRR4       R#   + '       g   i     EL; i  + '       g   i     ELe; i  + '       g   i     EL.; i  + '       g   i     L; i  + '       g   i     L; i  + '       g   i     R# ; i)rW   z3`x` and `y` must have the same length along `axis`.r   N"`x` and `y` must be broadcastable.(`x` and `y` must have length at least 2.z+This function does not support complex dataz"`method` must be an instance of...
asymptoticmethodexactrW   rE   r   )             y              y             )r   r   r   r[   r   r  )rc   rf   rg   messager   s   &    rm   test_input_validation"TestPearsonr.test_input_validationL  s   CG]]:W55NN1  6 F6]]:W55NN1  6 CC<]]:W55NN1  6 ?]]:W55NN1  6 7]]:W55NNAq6Aq6,? 6 nnaVaV,]]:W55##7#3 655 655 655 655 65 65 655sG   G;G.HHH)=H<G+	.G?	H	H&	)H9	<I	z-Monte Carlo method needs > a few kB of memoryr  method_namec           	     D   \         P                  P                  R 4      pVR8X  d   RMRpVP                  VR7      pVP                  VR7      pR\        P
                  ! VR7      R\        P                  ! VP                  3^,          R7      R\        P                  ! RR7      /pWq,          p\        P                  ! WVW(RR7      p	\        P                  ! WVVRR	7      p
\        V	P                  V
P                  R
R7       \        V	P                  V
P                  RRR7       VR8X  ds   \        P                  ! RR7      p\        P                  ! WVW(RR7      p\        VP                  V	P                  4       \        VP                  V	P                  4       R# R# )l   o#[mpermutationsizerngmonte_carlorvsmonte_carlo2i  )r  r  r?   r  r?   rD  r  {Gz?MbP?r  rF  NrE   d   )rE     rU   )r   randomdefault_rngnormalr[   PermutationMethodMonteCarloMethodr   r
   r>  r=  r   )rc   r  r  r  r  rf   rg   methodsr  r   refres2s   &&&         rm   test_resampling_pvalue#TestPearsonr.test_resampling_pvaluen  s6    ii##$56&-7xYJJDJ!JJDJ! %"9"9c"B %"8"8cjj]1_"M!5#9#9d#CE %nnQ{PRSnnQ{Ds}}5A

CJJTE.(++5F>>!KUWXD7cjj1	 )rp   c                .   \         P                  P                  R 4      pVP                  R
R7      pVP                  R
R7      p\        P
                  ! W4VRR7      p\         P                  P                  R4      p\        P                  ! VR7      pVP                  VR7      pVP                  4       p\        WxRR7       \         P                  P                  R4      p\        P                  ! VR7      pVP                  VR7      p	\        W4       R	# )l   _Y F r  r  l   |#(AkPrandom_stater  gQ?rE  r  Nr  rU   )	r   r  r  r  r[   r   BootstrapMethodr  r
   )
rc   r  r  rf   rg   r   r  res_ciref_cires_ci2s
   &&        rm   test_bootstrap_ciTestPearsonr.test_bootstrap_ci  s     ii##$45JJHJ%JJHJ%nnQ{D ii##$67&&C8(((7((*V4 ii##$67&&3/)))8(rp   r?   c                   \         P                  P                  R 4      pRpVP                  RV,           R7      w  rE\        P
                  ! WEVR7      pVP                  4       pV^ 8X  d   VP                  VP                  rT\        VP                  ^ ,          4       F  p\        P
                  ! WH,          WX,          4      p	V	P                  4       p
\        VP                  V,          V	P                  4       \        VP                  V,          V	P                  4       \        VP                  V,          V
P                  4       \        VP                  V,          V
P                  4       K  	  R# )   I.v# r  r>   NrI   rO   rE   )r   r  r  r  r[   r   r  r   rangeshaper
   r>  r=  r  r  )rc   r?   r  r  rf   rg   r   r  ires_ici_is   &&         rm   test_axis01TestPearsonr.test_axis01  s    ii##K0zzte|z,nnQ-$$&1933qqwwqz"ANN14.E,,.DCMM!,eoo>CJJqM5<<8BFF1Itxx0BGGAJ		2 #rp   c                   \         P                  P                  R 4      pRpVP                  RV,           R7      w  r4\        P
                  ! W4RR7      pVP                  4       p\        P
                  ! VP                  4       VP                  4       4      pVP                  4       p\        VP                  VP                  4       \        VP                  VP                  4       \        Wh4       R# )r  r  Nr>   r  r  )r   r  r  r  r[   r   r  ravelr
   r>  r=  )	rc   r  r  rf   rg   r   r  r  ci_refs	   &        rm   test_axis_NoneTestPearsonr.test_axis_None  s    ii##K0zzte|z,nnQ-$$&nnQWWY	2((*s}}5

CJJ/#rp   c                   VP                  R4      ;r#Rp\        P                  ! \        VR7      ;_uu_ 4        \        P
                  ! W#RR7       RRR4       Rp\        P                  ! \        VR7      ;_uu_ 4        \        P
                  ! W!P                  R4      ^R7       RRR4       Rp\        P                  ! \        VR7      ;_uu_ 4        \        P
                  ! VP                  R4      VP                  R4      ^R7       RRR4       Rp\        P                  ! \        VR7      ;_uu_ 4        \        P
                  ! W!P                  R4      ^R7       RRR4       R	p\        V4      '       gl   VP                  ^
4      p\        P                  ! \        VR7      ;_uu_ 4        \        P
                  ! W"\        P                  ! 4       R
7       RRR4       R# R#   + '       g   i     EL; i  + '       g   i     ELa; i  + '       g   i     EL; i  + '       g   i     L; i  + '       g   i     R# ; i)rE   z`axis` must be an integer.r   r2   r>   Nz2`x` and `y` must have the same length along `axis`r  r  z:`method` must be `None` if arguments are not NumPy arrays.r  r   rE   rW   r   rw   )	onesr   r   r   r[   r   r)   r   r  )rc   rd   rf   rg   r  s   &&   rm   test_nd_input_validation%TestPearsonr.test_nd_input_validation  sk   .]]:W55NN1c* 6 G]]:W55NN1ggfoA6 6 =]]:W55NN2776?BGGFO!D 6 7]]:W55NN1ggfoA6 6 O||		"Az99qE,C,C,EF :9 ! 655 655 655 65 :99s;   G, (H 8H<(H(4,H;,G=	 H	H%	(H8	;I	c                   \         P                  P                  R 4      pVP                  R
4      VP                  R
4      rCRp\        P                  ! \
        P                  VR7      ;_uu_ 4        ^^uVR&   VR&   VP                  V4      VP                  V4      rv\
        P                  ! Wg^R7      pVP                  4       p	VP                  VP                  VP                  .VP                  R7      p
\        VP                  R,          V
4       \        VP                  R,          V
4       \        V	P                  R,          V
4       \        V	P                   R,          V
4       VP#                  VP%                  VP                  R,          4      4      '       g   Q hVP#                  VP%                  VP                  R,          4      4      '       g   Q hVP#                  VP%                  V	P                  R,          4      4      '       g   Q hVP#                  VP%                  V	P                   R,          4      4      '       g   Q h RRR4       Rp\        P                  ! \
        P&                  VR7      ;_uu_ 4        RRuVR&   VR&   VP                  V4      VP                  V4      rv\
        P                  ! Wg^R7       RRR4       VP                  ^^.^^.^^.^R	..4      pVP                  ^^.^^.^^.^R	..4      pVP)                  ^4      p\
        P                  ! WgRR7      pVP                  4       p	\+        VP                  VP                  . RO4      4       \+        VP                  V4       \+        V	P                  V) 4       \+        V	P                   V4       R#   + '       g   i     ELm; i  + '       g   i     EL; i)l   U!Jr[  r   r>   r6   ry   rE   NrE   NNNz!An input array is nearly constantr   r   rw   )ry   .)rW   .g     ?g      @ry   ry   rW   rW   rU   )rW   rU   rU   r   )r   r  r  r   rb  r[   rc  rY   r   r  rb   r   r0   r>  r=  r  r  allisfiniterk  r  r/   )rc   rd   r  x0y0r  rf   rg   r   r  nansr  s   &&          rm   test_nd_special_cases"TestPearsonr.test_nd_special_cases  s   ii##N3F#SZZ%7B.\\%44GDD%&"BvJ6
::b>2::b>q..A.C((*B::rvvrvv.bjj:ADCMM#.5CJJsOT2BFF3K.BGGCL$/66"++cmmB&78999966"++cjjn5666666"++bffRj1222266"++bggbk23333 E 6\\%88HH!*IBtHbh::b>2::b>qNN1a( I JJAAAB89JJAAAB89wwqznnQ+$$&rzz/'BC

D)&&= EDD  IHHs,   1E+N68N68N6N6
AO
6O	
O	c                (   \         P                  P                  R 4      pVP                  R4      pVP                  ^
4      p\        P                  ! W4^R7      p\        P                  ! W4RR7      p\        VP                  VP                  4       R# )l   [LYr>   N)r   rO   rU   )r   r  r  r[   r   r   r>  rc   rd   r  rf   rg   r   r  s   &&     rm   test_different_dimensionality*TestPearsonr.test_different_dimensionality  sf     ii##$56JJwJJrNnnQ*nnQ+S]]CMM2rp   Nc                   \         P                  RR7      w  rE\        P                  ! VP	                  V4      VP	                  V4      W#R7      p\        P                  ! WEW#R7      p\        VP                  VP	                  VP                  4      4       \        VP                  VP	                  VP                  4      4       VP                  4       pVP                  4       p	\        VP                  VP	                  V	P                  4      4       \        VP                  VP	                  V	P                  4      4       R# )rE   r  r?   r  N)rE   rO   rP   )r  r  r[   r   rY   r/   r>  r=  r  r  r  )
rc   rd   r?   r  rf   rg   r   r  r  r  s
   &&&&      rm   test_array_apiTestPearsonr.test_array_api	  s     zz{z+nnRZZ]BJJqM"&AnnQFrzz#--'@A

BJJszz$:;((*((*

BJJvzz$:;RZZ%<=rp   r   ))	two-sided?gmgƎ?rW   )r  K˅?rU   g?
?rW   )r  .?gդζrW   rW   )r  r  gfǎgl?rU   )r  r	  rP  gդζ?rU   )r  r  g?
r   rU   r  r  r  )r  r  r  )ry   rW   N)&r   r   r   r   rA  rM  rQ  rX  rf  r   r   parametrizerm  rs  rv  r{  r  r  r   r  r   r  r  r  r  	fail_slowxfail_on_32bitr  slowr  r  r  r  r  r   r  r   r   r   s   @rm   r7  r7    s$    5PP/	3 [[Wy)&<=
! >
!MOL## [[ LM
3 N
3& d#[[CHI6I $6F# 4D [[2[[ OP[[],LM[[]KM2M N Q 
2( [[[[],LM) N )& [[VaV,3 -3 
$G0 [[ LM#' N#'J3$ [[V\2[[],LM> N 3>rp   r7  c                   v  a  ] tR tRt o Rt]P                  P                  ]P                  ! 4       R8H  RR7      R 4       t
R tR tR	 t]P                  P                  R
 4       tR tR tR tR t]P                  P)                  R. RO4      R 4       tR t]P                  P/                  ^
4      ]P                  P                  4       R 4       4       t]P                  P/                  ^
4      ]P                  P                  4       R 4       4       t]P                  P5                  4       R 4       tRtV tR# )TestFisherExacti  a  Some tests to show that fisher_exact() works correctly.

Note that in SciPy 0.9.0 this was not working well for large numbers due to
inaccuracy of the hypergeom distribution (see #1218). Fixed now.

Also note that R and SciPy have different argument formats for their
hypergeometric distribution functions.

R:
> phyper(18999, 99000, 110000, 39000, lower.tail = FALSE)
[1] 1.701815e-09
ppcztest known to fail on powerpcr   c                F   \         P                  pV! R R.RR..4      ^,          p\        VR^R7       V! ^d^.R^..4      ^,          p\        VR^R7       V! ^^.^^..4      ^,          p\        VR^R7       V! ^^.^
^
..4      ^,          p\        VR	^R7       V! ^^.^^..4      ^,          p\        VR
^R7       V! ^^.^^..4      ^,          p\        VR^R7       V! ^
^.^
^..4      ^,          p\        VR	^R7       V! ^^ .^^..4      ^,          p\        VR^R7       V! ^ ^.^^..4      ^,          p\        VR4       V! ^ ^.^^..4      ^,          p\        VR4       V! ^^.^^..4      p\        V^,          R^R7       \        V^ ,          R4       R# )8   N  0u  @  g؞Y?significantr  g,Ԛ?g2c?gY
A?g_?gO^M?gօa?r   ggE?Ng$I$I?)r[   fisher_exactr	   )rc   r  r   s   &  rm   rX  TestFisherExact.test_basic'  s   ))UENUEN;<Q?Ca8S!HtQi01!4CQ7QFQF+,Q/C:QFRH-.q1C:QGb"X./2C:QGb"X./2C:RGb!W-.q1C:QFQF+,Q/C;QFQF+,Q/C%QFQF+,Q/C.QFQF+,CFI1=CFH-rp   c                   ^d^.R^..R3^^.^^..R3^^.^
^
..R	3^^.^^..R
3^^.^^..R3^
^.^
^..R3^
^.^
^ ..R3^^ .^^..\         P                  R33^ ^.^^..R3^^.^ ^..\         P                  R33^ ^.^^..R3.pV F`  w  r#\        P                  ! \         P                  ! V4      4      p\         P
                  P                  V^,          V^,          ^RR7       Kb  	  R# )r  r  gaa?gaa?T)decimalverboseN)gAn&	?g}K
T?)g	7?g?)g!@j)A?)gU!a?gKY?)g7X?g~ltP?)gFu|?r  )r   gQN^?r   r   )r   infr[   r  rY   testingr   )rc   tablisttableres_rr   s   &    rm   test_preciseTestFisherExact.test_preciseC  s^    Ahq	"$TU!fq!fOP!fr2h!QR"gBx "RS"gBx "RS1gAw!QR1gAw!QR!fq!f(>?@!fq!fOP!fq!f(>?@!fq!fOP $LE$$RZZ%67CJJ**3q658R37 + 9 $rp   c                ,   ^^%.^l^..p\         P                  ! V4      p\        V^,          R4       ^^ .^ ^f..p\         P                  ! V4      p\        V^,          R4       ^^^0.RR..p\         P                  ! V4      p\        V^,          R4       R# )rz   gmt?g,:i  i\B  gNQ8Nr[   r  r
   rc   rf   r   s   &  rm   test_gh4130TestFisherExact.test_gh4130[  s     WsCj!  #A 12 !Wq#h  #A 56 "Xe}%  #A 56rp   c                l    R R.RR..p\         P                  ! V4      p\        V^,          ^ RR7       R# )iiX iV iW gѧRrE  Nr)  r*  s   &  rm   test_gh9231TestFisherExact.test_gh9231q  s8     w'7!34  #A/rp   c                    . ROp\        V. RO4       F5  w  r#\        P                  ! RR.RV..4      ^,          p\        WB^R7       K7  	  \        P                  ! RR.RR..4      ^,          p\        VR	^R7       R
# )?=i(E  i  i)  r  iPF  i8 r  i_ g^K=?N)r1  gNuP=gs=)K   L   M   )zipr[   r  r	   )rc   pvalsr  numr   s   &    rm   test_large_numbers"TestFisherExact.test_large_numbersx  sx     1UL1ID$$uclT3K%@A!DCq9 2   5%.5%.!AB1ECQ7rp   c                    R p\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! \
        P                  ! ^4      4       RRR4       R#   + '       g   i     R# ; i)z+The input `table` must have two dimensions.r   N)r   r   r   r[   r  r   r   rc   r  s   & rm   test_raisesTestFisherExact.test_raises  s=    ?]]:W55ryy|, 6555s   +AA-	c                    ^ ^ .^^
..^^
.^ ^ ..^ ^.^ ^
..^^ .^
^ ..3pV FA  p\         P                  ! V4      w  r4\        VR4       \        V\        P                  4       KC  	  R# r   )r[   r  r   r   rb   )rc   tablesr$  	oddsratior  s   &    rm   test_row_or_col_zero$TestFisherExact.test_row_or_col_zero  s    q6Ar7#r7QF#q6Ar7#q6B7#% E#007OIs#BFF+ rp   c                   ^^.^^..^^.^R..^^.^R..^R.^R..^ ^.^^ ..^^.^^..^^ .^^..^ ^.^^..^^ .^^..3	pRR.RR.RR	.R
R.RR.RR.RR.RR.RR.3	p\        W4       Fq  w  r4. pVP                  \        P                  ! VRR7      ^,          4       VP                  \        P                  ! VRR7      ^,          4       \	        WT^ RR7       Ks  	  R# )rE   i,  i  i   i  gI[?gq}!?r   g2\&gQp6g:O_?g a?皙?ffffff??333333?r  r  r  r  )rF  r  NUUUUUU?rV  )r5  appendr[   r  r
   )rc   r?  r6  r$  r  r   s   &     rm   test_less_greater!TestFisherExact.test_less_greater  sL    VaV1X3x "X4y!3Z#s$ VaVVaVVaVVaVVaV  "#56)*()	"#J#J#J3K$K v-KECJJu))%VDQGHJJu))%YGJKCAD9	 .rp   c                B    \         P                  ! ^^.^	R..4      w  rR# )rW   i"N)r[   r  )rc   oddsr=  s   &  rm   test_gh3014TestFisherExact.test_gh3014  s%     ))Aq6Ax=*ABfrp   r  c                    \         P                  ! R R.RR..4      p\        P                  ! W!R7      p\	        VP
                  VP                  3V4       R# )r  r  r  r  r  N)r   r   r[   r  r   r>  r=  )rc   r  r$  r   s   &&  rm   test_resultTestFisherExact.test_result  sD    5%.5%.9:  @cmmSZZ0#6rp   c                   \         P                  P                  R 4      p\         P                  ! ^^.^^..4      pRp\        P
                  ! \        VR7      ;_uu_ 4        \        P                  ! VR7      p\        P                  ! W$RR7       RRR4       Rp\        P
                  ! \        VR7      ;_uu_ 4        \        P                  ! VR7      p\        P                  ! W$R7       RRR4       R	p\        P
                  ! \        VR7      ;_uu_ 4        \        P                  ! \        P                  P                  R
7      p\        P                  ! W$R7       RRR4       Rp\        P
                  ! \        VR7      ;_uu_ 4        \        P                  ! \         P                  ! R4      4       RRR4       \         P                  P!                  \        P                  ! . RO.4      R4       \         P                  P!                  \        P                  ! ^.^.^..4      R4       \         P                  P!                  \        P                  ! \         P                  ! R4      4      R4       R#   + '       g   i     EL; i  + '       g   i     EL; i  + '       g   i     ELM; i  + '       g   i     EL; i)   9o8o z4`alternative` must be the default \(None\) unless...r   r  r  r  r  Nz6...not recognized; if provided, `method` must be an...r  z3If the `method` argument of `fisher_exact` is an...r  z2`table` must have at least one row and one column.ry   rW   r  r  rE   r   )r   r  r  rY   r   r   r   r[   r  r  r  r  normr  zerosr"  r   )rc   r  r$  r  r  s   &    rm   $test_input_validation_edge_cases_rxc4TestFisherExact.test_input_validation_edge_cases_rxc  s   ii##$78

QFQF+,I]]:W55,,5FuH 6 K]]:W55**s3Fu4 6 H]]:W55++

?Fu4 6 G]]:W55rxx/0 6
 	

 2 2I; ?H


 2 2QC!qc? CVL


 2 2288F3C DfM- 655
 655
 655
 655s1   "0J  /JAJ(+J< J	J%	(J9	<K	c                   \         P                  P                  R 4      p\         P                  ! ^^.^^..4      p\        P
                  ! V4      pVP                  p\        P                  ! VP                  ^R7      VP                  ^ R7      4      P                  V4      p\        P                  ! VR7      p\        P
                  ! W&R7      p\        VP                  VRR7       \        VP                  V4       \        P                  ! VR7      p\        P
                  ! W&R7      p\        VP                  VP                  RR7       \        VP                  V4       R# )rT  r>   r  r  g{Gzd?rE  N)r   r  r  rY   r[   r  r=  random_tablesumpmfr  r
   r   r>  r  )rc   r  r$  r  
ref_pvalueref_statr  r   s   &       rm   test_resampling_2x2#TestFisherExact.test_resampling_2x2  s    ii##$78

QFQF+,  'ZZ
%%eiiQi&79JKOOPUV''C0  6

JV<S]]H-((S1  6

CJJV<S]]H-rp   c                   . R
O. RO. RO. RO. RO.p\         P                  ! V4      pRp\         P                  P                  R4      p\        P
                  ! VR7      p\        P                  ! WR7      p\        VP                  VRR7       \        P                  ! VRR7      p\        P                  ! WR7      p\        VP                  VRR7       R	# )rW   gk$?l   |Kr  r  gMb@?rE  i )r  n_resamplesN)rW   rE   rE   rW   rW   ry   rW   )rE   ry   ry   rE   r   ry   ry   )ry   rW   rW   rW   rE   rJ   r   )rW   rW   rE   ry   ry   ry   rW   )ry   rW   rW   rW   rW   ry   ry   )
r   rY   r  r  r[   r  r  r
   r=  r  )rc   r$  r`  r  r  r   s   &     rm   test_resampling_rxc#TestFisherExact.test_resampling_rxc  s     '&&&&	(
 

5!%
ii##M2((S1  6

JT:''CUC  6

JT:rp   c           
        \         P                  P                  R 4      p\        P                  ! VR7      p\        ^^4       F  p\        ^^4       F  p\        ^^4       F  p\        ^^4       Fl  p\         P                  ! W4.WV..4      p\        P                  ! V4      p\        P                  ! WrR7      p	\        V	P                  VP                  RR7       Kn  	  K  	  K  	  K  	  R# )rT  r  r  +=rE  N)
r   r  r  r[   r  r  rY   r  r
   r=  )
rc   r  r  rK  rW  cdr$  r  r   s
   &         rm   test_resampling_exact_2x2)TestFisherExact.test_resampling_exact_2x2  s     ii##$78((S1q!A1a[q!A"1a[ "

QFQF+; <#007#00F'

CJJUK	 ) % ! rp   r   Nr  r  r  )r   r   r   r   r5  r   r   skipifplatformmachinerX  r&  r+  r.  r  r8  r<  rA  rJ  rN  r  rQ  rZ  r  rb  rf  xslowrl  r   r   r   s   @rm   r  r    sE     [[((*E1:YZ. [.6907,0 [[8 8-, :DC
 [[],LM7 N7
N> [[2[[.  ." [[2[[;  ;: [[L Lrp   r  c                      a  ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR t R t!R  t"R! t#R" t$R# t%R$ t&R%t'V t(R&# )'TestCorrSpearmanri!  r   c                    \         P                  ! R R4      p\        \        P                  ! V4      P                  4       4       R# )r   r   N)r[   	spearmanrr   r   isnanr  )rc   rg   s   & rm   test_scalarTestCorrSpearmanr.test_scalar*  s)    OOB#!"rp   c                    \        \        \        P                  . RO^^	.4       \        \        \        P                  . RO^4       R# rW   N)rW   rE   rW   )r   r   r[   rv  rc   s   &rm   test_uneven_lengths%TestCorrSpearmanr.test_uneven_lengths.  s*    j%//9q!fEj%//9a@rp   c                `   \         P                  P                  R 4       \         P                  P                  ^^4      p\         P                  P                  ^^4      p\        P
                  ! W4      P                  P                  R8X  g   Q h\        P
                  ! VP                  VP                  ^R7      P                  P                  R8X  g   Q h\        \        \        P
                  W^R7       \        \        \        P
                  VP                  VP                  4       R# )鄋 r>   Nrw   rw   )r   r  seedrandnr[   rv  r>  r  r   r=  r   r   rc   rf   rg   s   &  rm   test_uneven_2d_shapes'TestCorrSpearmanr.test_uneven_2d_shapes2  s    
		vIIOOAq!IIOOAq!q$..44>>>qssACCa077==GGGj%//1a@j%//133<rp   c           	        \         P                  P                  R 4       \         P                  P                  ^^^4      p\	        \
        \        P                  V4       \	        \
        \        P                  W4       \	        \
        \        P                  VRR4       \        \        P                  ! WRR7      \        P                  ! VP                  4       VP                  4       ^ R7      4       R# )r  Nr>   )
r   r  r  r  r   r   r[   rv  r
   flattenrc   rf   s   & rm   test_ndim_too_high$TestCorrSpearmanr.test_ndim_too_high=  s    
		vIIOOAq!$j%//15j%//18j%//1dDA48		QYY[qI	Krp   c                   \         P                  ! R 4      p\         P                  V^	&   \        \        P
                  ! W4      \         P                  \         P                  34       \        \        P
                  ! WRR7      R4       \        \        \        P
                  WRR7       \        \        \        P
                  WRR7       R# )r   r   r   r   r   N)r   r   )r   r   rb   r   r[   rv  r   r   r  s   & rm   test_nan_policy!TestCorrSpearmanr.test_nan_policyG  sx    IIcNvv!5??102662662BC5??1FC%	'j%//1GLj%//1HMrp   c                6   \         P                  P                  ^4       \         P                  P                  ^^
4      p^p\         P                  VRV3&   \         P
                  ! W^R7      p\        P                  ! VRR7      w  rE\        P                  ! V4      w  rg\         P
                  ! \         P
                  ! WB^R7      V^ R7      p\         P
                  ! \         P
                  ! WR^R7      V^ R7      p\        WFRR7       \        WWRR7       R# )rw   r   r>   r   r   ri  rE  N)	r   r  r  randrb   deleter[   rv  r
   )rc   rf   krg   corxpxcorypys   &       rm   test_nan_policy_bug_12458+TestCorrSpearmanr.test_nan_policy_bug_12458P  s    
		qIINN1b!&&!Q$IIa#??18??1%yy43QQ?YYryyQ/;/U+rp   c                    \         P                  P                  ^4       ^p^
p\         P                  P                  W4      p\         P                  VR&   \         P                  VR&   \
        P                  ! V^RR7      w  rE\        V4       UUu. uFM  p\        V4       Uu. uF4  p\
        P                  ! W7R3,          W6R3,          4      P                  NK6  	  upNKO  	  ppp\        WH4       R# u upi u uppi )rw   	propagater?   r   r   NrW   ry   )r   rU   )
r   r  r  r  rb   r[   rv  r  r>  r
   )	rc   mnrf   corrr=  jr  r   s	   &        rm   test_nan_policy_bug_12411+TestCorrSpearmanr.test_nan_policy_bug_12411]  s    
		qIIOOA!&&$66%qq[Ia" 1 FK1XNXQ$a41;;XN  	 "" O "s   C:$:C5C:5C:c                n    \         P                  ! \        \        4      pV^ ,          p\        VR4       R# r   )r[   rv  rZ   r	   r   s   &  rm   test_sXXTestCorrSpearmanr.test_sXXi  s%    OOAa aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   rv  rZ   r   r	   r   s   &  rm   
test_sXBIGTestCorrSpearmanr.test_sXBIGn  s%    OOAc"aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   rv  rZ   r   r	   r   s   &  rm   test_sXLITTLETestCorrSpearmanr.test_sXLITTLEs  s%    OOAf%aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   rv  rZ   r   r	   r   s   &  rm   test_sXHUGETestCorrSpearmanr.test_sXHUGEx  %    OOAd#aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   rv  rZ   r   r	   r   s   &  rm   test_sXTINYTestCorrSpearmanr.test_sXTINY}  r  rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   rv  rZ   r  r	   r   s   &  rm   test_sXROUNDTestCorrSpearmanr.test_sXROUND  s%    OOAe$aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\        VR4       R# r   )r[   rv  r   r	   r   s   &  rm   test_sBIGBIGTestCorrSpearmanr.test_sBIGBIG  s%    OOC$aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   rv  r   r   r	   r   s   &  rm   test_sBIGLITTLE!TestCorrSpearmanr.test_sBIGLITTLE  s%    OOC'aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   rv  r   r   r	   r   s   &  rm   test_sBIGHUGETestCorrSpearmanr.test_sBIGHUGE  %    OOC%aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   rv  r   r   r	   r   s   &  rm   test_sBIGTINYTestCorrSpearmanr.test_sBIGTINY  r  rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   rv  r   r  r	   r   s   &  rm   test_sBIGROUND TestCorrSpearmanr.test_sBIGROUND  s%    OOC&aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\        VR4       R# r   )r[   rv  r   r	   r   s   &  rm   test_sLITTLELITTLE$TestCorrSpearmanr.test_sLITTLELITTLE  s%    OOF6*aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   rv  r   r   r	   r   s   &  rm   test_sLITTLEHUGE"TestCorrSpearmanr.test_sLITTLEHUGE  %    OOF4(aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   rv  r   r   r	   r   s   &  rm   test_sLITTLETINY"TestCorrSpearmanr.test_sLITTLETINY  r  rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   rv  r   r  r	   r   s   &  rm   test_sLITTLEROUND#TestCorrSpearmanr.test_sLITTLEROUND  s%    OOF5)aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\        VR4       R# r   )r[   rv  r   r	   r   s   &  rm   test_sHUGEHUGE TestCorrSpearmanr.test_sHUGEHUGE  %    OOD&aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   rv  r   r   r	   r   s   &  rm   test_sHUGETINY TestCorrSpearmanr.test_sHUGETINY  r  rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   rv  r   r  r	   r   s   &  rm   test_sHUGEROUND!TestCorrSpearmanr.test_sHUGEROUND  %    OOD'aDAc"rp   c                n    \         P                  ! \        \        4      pV^ ,          p\        VR4       R# r   )r[   rv  r   r	   r   s   &  rm   test_sTINYTINY TestCorrSpearmanr.test_sTINYTINY  r  rp   c                n    \         P                  ! \        \        4      pV^ ,          p\	        VR4       R# r   )r[   rv  r   r  r	   r   s   &  rm   test_sTINYROUND!TestCorrSpearmanr.test_sTINYROUND  r  rp   c                n    \         P                  ! \        \        4      pV^ ,          p\        VR4       R# r   )r[   rv  r  r	   r   s   &  rm   test_sROUNDROUND"TestCorrSpearmanr.test_sROUNDROUND  s%    OOE%(aDAc"rp   c                    \         P                  ! \        \        4      pRp\        W4       \	        VP
                  VP                  4       R# r:  )r[   rv  rZ   r   r   r;  r>  r?  s   &  rm    test_spearmanr_result_attributes2TestCorrSpearmanr.test_spearmanr_result_attributes  s1    ooa#.
C,S__cmm4rp   c                    . ROp. ROp\         P                  ! W4      p\         P                  ! \        P                  ! W.4      P                  4      p\        W44       R# )rW   NrW   rE   r   r   rw   rz   )rW   rE   r   r   rz   rw   )r[   rv  r   rY   r   r
   rc   x1x2res1r  s   &    rm   test_1d_vs_2dTestCorrSpearmanr.test_1d_vs_2d  sA    r&rzz2(3556#rp   c                $   R F  p^\         P                  ^^^^.p^^^^^\         P                  .p\        P                  ! W#VR7      p\        P                  ! \         P                  ! W#.4      P
                  VR7      p\        WE4       K  	  R# )r  r   N)r  r   )r   rb   r[   rv  rY   r   r
   )rc   r   r  r  r  r  s   &     rm   test_1d_vs_2d_nans$TestCorrSpearmanr.test_1d_vs_2d_nans  sq    /JRVVQ1a(BQ1a(B??2jAD??2::rh#7#9#9jQDD' 0rp   c                   \         P                  ! ^4      pV) p\         P                  ! . RO4      p\         P                  ! WV.4      P                  p\
        P                  ! V4      p\         P                  ! . RO. RO. RO.4      p\         P                  ! R\        R7      pRVR	&   RVR
&   \        VP                  V4       \        VP                  V4       R# )rz   r6   g+Hs]s?N)ry   rW   rE   r   rw   r   )rW   rU   3+?)rU   rW   3+)r  r  rW   )r   r   )rE   r  )r  rE   )r   r   r   rY   r   r[   rv  rY  floatr
   r>  r=  )rc   r  r  x3rf   actualexpected_correxpected_pvalues   &       rm   
test_3colsTestCorrSpearmanr.test_3cols  s    YYq\SXX()JJ|$&&#"5"6">"@ A ((67"/"/((-87rp   c           
        \         P                  ! \         P                  R RRRRR.R\         P                  RRRRR.. RO.4      P                  p\         P                  ! \         P                  \         P                  \         P                  .\         P                  \         P                  \         P                  .\         P                  \         P                  R	..4      p\	        \
        P                  ! VR
R7      P                  V4       \
        P                  ! VRR7      P                  p\	        V^ ,          ^,          V^ ,          ^,          V^,          ^,          3RRR7       R# )r   r   r8   ffffff@r   ffffff"@ffffff@g333333@皙@r   r  r   r   r  r  N)r1   r   ffffff@ffffff@r   r   ffffff@)gacJC?g%ln?g_0nYt!޿)r   r   rb   r   r
   r[   rv  r>  )rc   rf   r  r   s   &   rm   test_gh_9103TestCorrSpearmanr.test_gh_9103  s   HHrvvsCc3<BFFCc3<9; <<=A 	
 xx"&&"&&"&&1&&"&&"&&1&&"&&"-/ 0 	kBLL	 ooaF3==QCF1Is1vay9:	Grp   c                   ^dp\         P                  P                  R4      pVP                  V4      pVP                  V4      R8  pVR8  p\         P                  ! V4      p\
        P                  ! WVRR7      P                  p\         P                  Wd&   \
        P                  ! WVRR7      P                  pVP                  \         P                  4      p\
        P                  ! WVRR7      P                  p	. ROp
\        WxV	.V
4       R# )r  iH rE  r1   r   r   N)gonj?)Wn%?r
  )r   r  RandomStater  r   r[   rv  r>  rb   astypeint32r
   )rc   r  r  rf   r  rK  rW  r  r  res3expecteds   &          rm   test_gh_8111TestCorrSpearmanr.test_gh_8111  s    ii##F+HHQKHHQK# VHHQKq7AA vvq7AA HHRXXq7AA:T*H5rp   r   N))r   r   r   r   r5  rx  r}  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r   r   s   @rm   rt  rt  !  s     #A	=KN,
##
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5$(8 G6 6rp   rt  c                      a  ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tR tR tR tR tR tR t]P*                  P-                  RR4      R 4       tRtV tR# )TestCorrSpearmanr2i  z-Some further tests of the spearmanr function.c                    . ROp. ROpRp\         P                  ! W4      p\        V^ ,          V^ ,          4       \        V^,          V^,          4       R# )rW   NrW   rE   r   r   rw   rw   rz   rJ   rF   rJ   gh
C?gR?)r[   rv  r	   rc   r  r  r  r   s   &    rm   test_spearmanr_vs_r&TestCorrSpearmanr2.test_spearmanr_vs_r"  sE     >oob%CFHQK0CFHQK0rp   c                    \        \        P                  ! . . 4      \        P                  \        P                  34       R # N)r   r[   rv  r   rb   r|  s   &rm   test_empty_arrays$TestCorrSpearmanr2.test_empty_arrays,  s$    U__R,rvvrvv.>?rp   c           	        \         P                  P                  R 4      p\         P                  ! VP	                  ^^RR7      VP	                  ^^RR7      .4      pRR.RR..p\         P
                  ! \         P                  P                  V4      V4      pRp\        P                  ! V^ ,          V^,          4      p\        V^ ,          V^ ,          4       \        V^,          V^,          4       R# )z    locscaler  r   rG  N)gCzYW?ge*=)r   r  r  r   r  dotlinalgcholeskyr[   rv  r	   )rc   r  rf   r  r  r   s   &     rm   test_normal_draws$TestCorrSpearmanr2.test_normal_draws/  s    ii##D)HHcjjQacj:jjQacj:< =c
c
FF299%%d+Q/?ooadAaD)CFHQK0CFHQK0rp   c                ^    \        \        P                  ! . RO. RO4      ^ ,          R4       R# )rW   r   NrW   rW   rE   )r	   r[   rv  r|  s   &rm   test_corr_1TestCorrSpearmanr2.test_corr_1;  s    EOOIyA!DcJrp   c                   \         P                  ! R 4      p\         P                  V^	&   \        \        P
                  ! W4      \         P                  \         P                  34       \        \        P
                  ! WRR7      R4       \        \        \        P
                  WRR7       \        \        \        P
                  WRR7       R# )r   r   r   r   r   N)r   ry   )	r   r   rb   r   r[   rv  r
   r   r   r  s   & rm   test_nan_policies$TestCorrSpearmanr2.test_nan_policies>  sx    IIcNvv!5??102662662BC@ 	"j%//1GLj%//1HMrp   c                    \         P                  ! R 4      p\         P                  ! R4      p\        \        \        P
                  W4       R# )r         4@N)r   r   r   r   r[   rv  r  s   &  rm   test_unequal_lengths'TestCorrSpearmanr2.test_unequal_lengthsG  s,    IIcNIIcNj%//18rp   c                    . ROp^^^\         P                  .p\        P                  ! WRR7      p\        P                  ! VR,          VR,          RR7      p\	        W44       R# )rW   r   r   :Nr   NNr  )r   rb   r[   rv  r   r  s   &    rm   test_omit_paired_value)TestCorrSpearmanr2.test_omit_paired_valueL  sK    Arvvr&9r"vr"v&AT rp   c                   \        \        R 4      4      p\        \        R 4      4      pV^	,          V^ ,          uV^ &   V^	&   VR,          V^
,          uV^
&   VR&   VR,          VR,          uVR&   VR&   VP                  \        P                  4       VP                  R4       \        \        P                  ! WRR7      ^ ,          R4       R# )	  i  i  i  r   r   r   gV-?N)listr  rI  r   rb   r   r[   rv  r  s   &  rm   #test_gh_issue_6061_windows_overflow6TestCorrSpearmanr2.test_gh_issue_6061_windows_overflowS  s    ttqT1Q4
!ad#""qvD'1S6#$ 	
	EOOAVDQGOrp   c                   R p\         P                  ! \        P                  VR7      ;_uu_ 4        \        P                  ! . RO. RO4      w  r#\        V\        P                  4       \        V\        P                  4       \        P                  ! . RO. RO4      w  r#\        V\        P                  4       \        V\        P                  4       \        P                  ! . RO. RO4      w  r#\        V\        P                  4       \        V\        P                  4       RRR4       R#   + '       g   i     R# ; i)r[  r   NrE   rE   rE   rE   ry   rE   )r   rb  r[   rc  rv  r   r   rb   )rc   warn_msgr   re  s   &   rm   	test_tie0TestCorrSpearmanr2.test_tie0`  s    /\\%44HEE??9i8DABFF#BFF#??9i8DABFF#BFF#??9i8DABFF#BFF# FEEEs   C4D//E 	c                    . ROp. ROp. ROp. ROp\         P                  ! W4      p\         P                  ! W44      p\        WV4       R# )r   Nr   r   r   r   )r   r   r   r   )r   rt   rt   r   )r[   rv  r   r   )rc   rf   rg   xryrsrprs   &      rm   	test_tie1TestCorrSpearmanr2.test_tie1n  s<      !! __Q"^^B#B#rp   c                    . ROp. ROp^^R^\         P                  .p^^R^\         P                  .p\        P                  ! W4      p\        P                  ! W4RR7      p\	        WV4       R# )rW   rt   r   r   N)rW   rE   rt   rE   )rW   r   rt   r   )r   rb   r[   rv  r   )rc   r  rh   r  ri   sr1sr2s   &      rm   	test_tie2TestCorrSpearmanr2.test_tie2{  s^     CBFF#CBFF# oob%oob8C%rp   c                   \         P                  ! . RO. RO.4      p\         P                  ! . RO. RO.4      p\         P                  ! . RO. RO.4      pRp\        P                  ! \        P
                  VR7      ;_uu_ 4        \        P                  ! V^R7      w  rV\        V\         P                  4       \        V\         P                  4       \        P                  ! V^R7      w  rV\        V\         P                  4       \        V\         P                  4       \        P                  ! V^R7      w  rV\        V\         P                  4       \        V\         P                  4       RRR4       R#   + '       g   i     R# ; i)rW   r[  r   r>   NrW   rW   rW   rW   r  	r   r   r   rb  r[   rc  rv  r   rb   )rc   z1z2z3r@  r   re  s   &      rm   test_ties_axis_1#TestCorrSpearmanr2.test_ties_axis_1  s    XX|\23XX|\23XX|\23/\\%44HEE??2A.DABFF#BFF#??2A.DABFF#BFF#??2A.DABFF#BFF# FEEEs   C+E::F	c                   \         P                  ! . RO4      p\         P                  ! . RO4      pRp\        P                  ! \        P
                  VR7      ;_uu_ 4        \        P                  ! W4      w  rE\        V\         P                  4       \        V\         P                  4       RRR4       R#   + '       g   i     R# ; i)r   r[  r   N)
r   r   r   r   r   r   r   r   r   r   
ry   gN}	?ry   ry   g	/`?gY%uX-H?gC1tq1?ry   ry   g*I?rR  )rc   rf   rg   r@  r   re  s   &     rm   test_gh_11111 TestCorrSpearmanr2.test_gh_11111  s~    HHGHHH - . 0\\%44HEE??1(DABFF#BFF# FEEEs   !AB88C		c                    \         P                  ! . RO4      p\         P                  ! . RO4      p\        \        \        P
                  W^R7       R# )r   r>   N)
r   r   r   r   r   r   r   r   r   r   rY  )r   r   r   r   r[   rv  r  s   &  rm   test_index_error#TestCorrSpearmanr2.test_index_error  s8    HHGHHH - . 	j%//1a@rp   c                &   . ROp. R	OpR
p\         P                  ! WRR7      p\        V^ ,          V^ ,          4       \        V^,          ^V^,          ^,          ,
          4       \         P                  ! WRR7      p\        V^ ,          V^ ,          4       \        V^,          V^,          ^,          4       \        P                  ! \
        RR7      ;_uu_ 4        \         P                  ! WRR7       RRR4       R#   + '       g   i     R# ; i)rW   r  r  r  `alternative` must be 'less'...r   	ekki-ekkiNr  r  r  )r[   rv  r	   r   r   r   r  s   &    rm   test_alternative#TestCorrSpearmanr2.test_alternative  s      ? oob&9CFHQK0CFA!q$9: oob)<CFHQK0CFHQK!O4]]:-NOOOOB< POOOs   C??D	r  c           	        . R
Op. ROpV\         P                  .,           pV\         P                  .,           p\        \        P                  ! WE4      \         P                  \         P                  34       \        P                  ! WERVR7      p\        P                  ! W#VR7      p\        Wg4       Rp\        P                  ! \        VR7      ;_uu_ 4        \        P                  ! WERVR7       RRR4       Rp\        P                  ! \        VR7      ;_uu_ 4        \        P                  ! WER	VR7       RRR4       R#   + '       g   i     LZ; i  + '       g   i     R# ; i)rW   r   r   r  r  r   r   r   Nr   ra  r  r  )	r   rb   r   r[   rv  r
   r   r   r   )	rc   r  r  r  x1nanx2nan
res_actualres_expectedr  s	   &&       rm   test_alternative_nan_policy.TestCorrSpearmanr2.test_alternative_nan_policy  s     bffXbffX 	5??58266266:JK __Uf1<>
r;G
1 2]]:W55OOEW(35 6
 1]]:W55OOE[(35 65 65 655s   E!EE	E)	r   Nrn  )r   r   r   r   r5  r  r  r(  r,  r/  r3  r6  r;  rA  rI  rN  rV  rZ  r]  rb  r   r   r  rj  r   r   r   s   @rm   r  r    s     71@
1KN9
!P$$&$ 	$A=. [[],LM5 N5rp   r  c            	         R!p . R"Op. R#OpR$pV  FO  p\         P                  ! WVR7      p\        V^ ,          V^ ,          4       \        V^,          V^,          4       KQ  	  . R%Op. R&OpR$pV  FO  p\         P                  ! WVR7      p\        V^ ,          V^ ,          4       \        V^,          V^,          4       KQ  	  . R'Op. R(OpR)pV  FO  p\         P                  ! WVR7      p\        V^ ,          V^ ,          4       \        V^,          V^,          4       KQ  	  . R*Op. R+OpR,pV  FO  p\         P                  ! WVR7      p\        V^ ,          V^ ,          4       \        V^,          V^,          4       KQ  	  \        P                  ! ^
4      p\        P                  ! ^
4      pR-pV  FO  p\         P                  ! WVR7      p\        V^ ,          V^ ,          4       \        V^,          V^,          4       KQ  	  V^,          pV^,          V^&   Wb^&   R.pV  FO  p\         P                  ! WVR7      p\        V^ ,          V^ ,          4       \        V^,          V^,          4       KQ  	  V^,          pV^,          V^&   Wb^&   R/pV  FO  p\         P                  ! WVR7      p\        V^ ,          V^ ,          4       \        V^,          V^,          4       KQ  	  \        P                  ! ^
4      p\        P                  ! ^
4      RRR01,          pR1pV  FO  p\         P                  ! WVR7      p\        V^ ,          V^ ,          4       \        V^,          V^,          4       KQ  	  V^,          pV^,          V^&   Wb^&   R2pV  FO  p\         P                  ! WVR7      p\        V^ ,          V^ ,          4       \        V^,          V^,          4       KQ  	  V^,          pV^,          V^&   Wb^&   R3pV  FO  p\         P                  ! WVR7      p\        V^ ,          V^ ,          4       \        V^,          V^,          4       KQ  	  \        . R4O4      p\        . R5O4      pRp\        \         P                  ! WR R7      ^ ,          V4       Rp\        \         P                  ! WRR7      ^ ,          V4       V^,          V^&   \        \        \         P                  WRR7       \        \        \         P                  WR	R7       \        \        \         P                  WR
R7       . R6Op. R7OpR8p\         P                  ! Wx4      p\        V^ ,          V^ ,          4       \        V^,          V^,          4       R9p	V  FF  p\         P                  ! WxVR7      p\        WY4       \        VP                  VP                  4       KH  	  V  F  p\        \         P                  ! . R:O. R:OVR7      \        P                  \        P                  34       \        \         P                  ! . R;O. R:OVR7      \        P                  \        P                  34       \        \         P                  ! . R:O. R;OVR7      \        P                  \        P                  34       K  	  \        P                  ! \        RR7      ;_uu_ 4        \        \         P                  ! . . 4      \        P                  \        P                  34       RRR4       \        P                   P#                  R4      p
\        P
                  ! V
P%                  ^^RR7      V
P%                  ^^RR7      .4      pRR.RR..p\        P&                  ! \        P(                  P+                  V4      V4      pR<p\         P                  ! V^ ,          V^,          4      p\        V^ ,          V^ ,          4       \        V^,          V^,          4       \        \         P                  ! . R=O. R=OR R7      ^ ,          R4       \        \         P                  ! . R=O. R=ORR7      ^ ,          R4       \        P                  ! R4      p\        P                  V^	&   \-        \         P                  ! W4      \        P                  \        P                  34       \/        \         P                  ! WRR7      R>RR7       \/        \         P                  ! WRRR7      R?RR7       \        \        \         P                  WRR7       \        \        \         P                  WRR7       \        P                  ! R4      p\        P                  ! R4      p\        \        \         P                  W4       \        P                  ! \        RR7      ;_uu_ 4        \         P                  ! ^ .^ .4      w  rRRR4       \        \        P                  X4       \        \        P                  X4       \        P                  ! R\0        R7      p\        P2                  P5                  VR4      p\        P                  ! R\0        R7      p\        P6                  ! VR,          VR ,          34      p\9        \        P:                  ! \         P<                  P                  W4      ^,          4      4       R#   + '       g   i     EL; i  + '       g   i     EL; i)@rW  rj  r   )variantNgok|?gffffff?r  r  bananarmsOne or more sample...r   r   r!  r"  rG  g#q?r   r   r   r  r  r  )r   r  r   r   r2  r9  r6   i  :i  NN:Ni  N)rW  rj  )rw   rE   rW   r   rz   r   rJ   rF   )rw   rE   rz   r   rW   rF   rJ   r   r   )	ry   rw   rE   rW   r   rz   r   rJ   rF   )	rw   rE   ry   rz   r   rW   rF   rJ   r   )rw   rE   rW   r   rz   r   rJ   )rw   rE   rz   r   rW   rJ   r   )gJ$I¿gmK?)rE   rW   r   rz   r   rJ   rF   )rE   rz   r   rW   rF   rJ   r   )gJkaa?r   )r   紞xO~>)g?>?aV>)g}'}'?o&5>rU   )rP  rq  )g?>rr  )g}'}'rs  )
rW   rE   rE   r   r   rz   rz   rF   rI   rI   )
rW   rE   r   r   r   r   rF   rF   rF   rO   rQ   rE   rW   rQ   rE   rW   r   rJ   rW   ry   )g}+޿g`=i?r<  r>  r?  )g\zf?g^n)=r+  )r   g/>)r   g&?)r[   
kendalltaur	   r   r   r   r   r   r   r   r;  r>  rb   r   rb  r   r  r  r  r%  r&  r'  r   r
   r  mamasked_greaterconcatenater   r  mstats)variantsrf   rg   r  tauxr   rW  r  r  r@  r  r  taup_values                 rm   test_kendalltaur    se    H 	!A A HqT2CFHQK0CFHQK0  	$A#A HqT2CFHQK0CFHQK0  	AA /HqT2CFHQK0CFHQK0  	AA %HqT2CFHQK0CFHQK0  			"A
		"A )HqT2CFHQK0CFHQK0  	
!AQ4AaDaD 8HqT2CFHQK0CFHQK0  	
!AQ4AaDaD 8HqT2CFHQK0CFHQK0  			"A
		"ddA *HqT2CFHQK0CFHQK0  	
!AQ4AaDaD 9HqT2CFHQK0CFHQK0  	
!AQ4AaDaD 9HqT2CFHQK0CFHQK0  	,-A-.AH((s;A>IH((s;A>I Q4AaD*e..WE *e..XF *e..eD
 
B	B:H


2
"CA,A, +Jrt4C,S__cmm4  U%%iDIffbff%	'U%%iDIffbff%	'U%%iDIffbff%	'  
(0G	H	HU%%b"-/?@ 
I ))


%C
#**!#*6**!#*68 	9A#J#JD
ryy!!$'+A<H


1Q41
&CA,A, ((IsKAN((IsKAN"$ 			#A66AaDu''-/?@E$$Qf='e5E$$Qf\R1?*e..I*e..J 			#A
		#A*e..5 
(0G	H	H''aS1 
I! 			$e$A
Q%A
		$e$A
%!E(+,ABKK//4Q789a 
I	H	HL 
I	H	Hs   A kk2k/	2l	c                     \         P                  P                  ^*4      p \        ^^
4       F  p. p\        V4       F  pW#.V,          ,          pK  	  \	        V4      pV P                  V4       V P                  V4       \        P                  ! W$4      p\        P                  ! W$4      p\        V^ ,          V^ ,          4       \        V^,          V^,          4       K  	  R# *   N)
r   r  r  r  r:  shufflemstats_basicrw  r[   r	   )r  srK  r  rW  r  r  s          rm   test_kendalltau_vs_mstats_basicr    s    
))


#C1b\qAQJA GAA**10!!!'F1Ix{3F1Ix{3 rp   c                      . R	Op \         P                  RRR.p\        P                  ! WRR7      p\        P                  ! V R,          VR,          4      p\	        VP
                  VP
                  RR7       R# )
r   333333@333333@r   r   rW   NNrD  rE  NrD  )r   rb   r[   rw  r
   r>  )rf   rg   r1r2s       rm   test_kendalltau_nan_2nd_argr    sY    A	c3A			!6	2B			!B%2	'BBLL",,U;rp   c                     ^ RI p V P                  R4       . ROpR	pV P                  WR7      pV P                  WR7      p\        P                  ! W44      p\        VP                  R4       \        VP                  RRR7       R# )
ry   Ni_ r  g*8_2\S?gd`TR?gMb`?rE  rW   rE   r   r   rw   rz   rJ   i@ )r  r  choicesr[   rw  r
   r>  r=  )r  classes	n_samplesrf   rg   r   s         rm    test_kendalltau_gh18139_overflowr    sn    
 
KK#GIw,Aw,A


1
 CCMM#89 CJJT2rp   c            	       l  a  ] tR tRt o R tRt]P                  ]P                  ]P                  .t. ROt	. ROt
. ROt. ROt. ROt. ROt. ROt. ROtR t]! ]! ]]R.^,          4      4      ]! ]! ]]! ]4      R.^,          4      4      ,           t]P.                  P1                  R]4      R 4       t]! ]! ]]	R.^,          4      4      ]! ]! ]]! ]	4      R.^,          4      4      ,           t]P.                  P1                  R]4      R 4       t]! ]! ]]
R.^,          4      4      ]! ]! ]]! ]
4      R.^,          4      4      ,           t]P.                  P1                  R]4      R	 4       t]! ]! ]]R.^,          4      4      ]! ]! ]]! ]4      R.^,          4      4      ,           t]P.                  P1                  R]4      R
 4       t]! ]! ]]R.^,          4      4      ]! ]! ]]! ]4      R.^,          4      4      ,           t ]P.                  P1                  R] 4      R 4       t!]! ]! ]]R.^,          4      4      ]! ]! ]]! ]4      R.^,          4      4      ,           t"]P.                  P1                  R]"4      R 4       t#]! ]! ]]R.^,          4      4      ]! ]! ]]! ]4      R.^,          4      4      ,           t$]P.                  P1                  R]$4      R 4       t%]! ]! ]]R.^,          4      4      ]! ]! ]]! ]4      R.^,          4      4      ,           t&]P.                  P1                  R]&4      R 4       t']! ]! ]]R.^,          4      4      ]! ]! ]]! ]4      R.^,          4      4      ,           t(]P.                  P1                  R](4      R 4       t)]! ]! ]R.^,          4      4      ]! ]! ]R.^,          4      4      ,           t*]P.                  P1                  R]*4      R 4       t+]P.                  P1                  RR 4      ]P.                  P1                  RR!4      R 4       4       t,Rt-V t.R# )"TestKendallTauAlternativei  c                <   . R	Op. R
Op\         P                  ! WRR7      pV^ ,          ^ 8  g   Q h\         P                  ! WRR7      p\        V^ ,          V^ ,          4       \        V^,          ^V^,          ^,          ,
          4       \         P                  ! WRR7      p\        V^ ,          V^ ,          4       \        V^,          V^,          ^,          4       VP	                  4        \         P                  ! WRR7      pV^ ,          ^ 8  g   Q h\         P                  ! WRR7      p\        V^ ,          V^ ,          4       \        V^,          ^V^,          ^,          ,
          4       \         P                  ! WRR7      p\        V^ ,          V^ ,          4       \        V^,          V^,          ^,          4       \
        P                  ! \        RR7      ;_uu_ 4        \         P                  ! WRR7       RRR4       R#   + '       g   i     R# ; i)rW   r  r  r  r  r`  r   ra  Nr  r  )r[   rw  r   r
   reverser   r   r   r  s   &    rm   &test_kendalltau_alternative_asymptotic@TestKendallTauAlternative.test_kendalltau_alternative_asymptotic  s     ##BD{Q r6:SVXa[)AXa[1_ 56 r9=SVXa[)Aa0 	

 ##BD{Q r9=SVXa[)AXa[1_ 56 r6:SVXa[)Aa0]]:-NOOR= POOOs   'H

H	c                    V'       d!   \         P                  ! V4      ) pVR,          p\        P                  ! WRVR7      pWV3p\	        Wx4       R# )rW   r  rU  NrU   )r   rY   r[   rw  r
   )	rc   rf   rg   r  revstat_expected
p_expectedr   ri  s	   &&&&&&&  rm   
exact_test$TestKendallTauAlternative.exact_test0  sB    AARMqGM$0*rp   FTzalternative, p_expected, revc           
         ^.^.rT\         P                  p\        P                  ! \        RR7      ;_uu_ 4        V P                  WEWWb4       RRR4       R#   + '       g   i     R# ; i)rW   rp  r   N)r   rb   r   rb  r   r  rc   r  r  r  rf   rg   r  s   &&&&   rm   test_against_R_n1+TestKendallTauAlternative.test_against_R_n1;  sI    sQC1\\,4KLLOOA+MN MLLLs   AA)	c                >    ^^.^^.rTRpV P                  WEWWb4       R# )rW   g?Nr  r  s   &&&&   rm   test_against_R_n2+TestKendallTauAlternative.test_against_R_n2E  s&    1v1v1*kJrp   c                >    . RO. ROrT^pV P                  WEWWb4       R# rW   Nr  r  r  s   &&&&   rm   test_against_R_c0+TestKendallTauAlternative.test_against_R_c0N  s    )1kJrp   c                >    . RO. ROrTRpV P                  WEWWb4       R# )rW   gVUUUUU?Nr  )rW   rE   r   r   r  r  s   &&&&   rm   test_against_R_c1+TestKendallTauAlternative.test_against_R_c1W  s    \1*kJrp   c                >    . RO. ROrT^ pV P                  WEWWb4       R# )rW   Nr  )rW   rw   r   rE   r   r  r  s   &&&&   rm   test_against_R_no_correlation7TestKendallTauAlternative.test_against_R_no_correlationa  s    1kJrp   c                >    . RO. ROrT^ pV P                  WEWWb4       R# )rW   NrW   rE   r   r   rw   rz   rJ   rF   )rF   rz   rW   r   rE   rw   r   rJ   r  r  s   &&&&   rm   test_against_R_no_correlationb8TestKendallTauAlternative.test_against_R_no_correlationbk  s    ')A1kJrp   c                @    . ROp. ROpRpV P                  WEWWb4       R# )333333F@gqq?N)	r  g33333F@g33333D@gfffffJ@gYF@gF@gYI@gF@gN@)	g@@rt   r8   @r   g@ffffff@r  r  r  s   &&&&   rm   test_against_R_lt_171/TestKendallTauAlternative.test_against_R_lt_171t  s$     C9*kJrp   c                    \         P                  P                  ^ 4      pVP                  ^d4      pVP                  ^d4      pRpV P	                  WVWWr4       R# )ry   NgUm*,r   r  r  r  r  rc   r  r  r  r  rf   rg   r  s   &&&&    rm   test_against_R_lt_171b0TestKendallTauAlternative.test_against_R_lt_171b  sE    ii##A&HHSMHHSM,kJrp   c                    \         P                  P                  ^ 4      pVP                  ^4      pVP                  ^4      pRpV P	                  WVWWr4       R# )ry   gH4?Nr  r  s   &&&&    rm   test_against_R_lt_171c0TestKendallTauAlternative.test_against_R_lt_171c  sE    ii##A&HHSMHHSM*kJrp   zalternative, revc                X   \         P                  P                  ^ 4      pVP                  R4      pVP                  R4      p\        P
                  ! WERVR7      p\        P
                  ! WERVR7      p\        V^ ,          V^ ,          4       \        V^,          V^,          RR7       R# )ry   r8  r  rU  r  r  r  N)r   r  r  r  r[   rw  r   r
   )rc   r  r  r  rf   rg   res0r  s   &&&     rm   test_gt_171%TestKendallTauAlternative.test_gt_171  s    ii##A&HHSMHHSMW,79\,79T!Wd1g&Qat4rp   r  r  c           
        . R
Op. ROpV\         P                  .,           pV\         P                  .,           p\        P                  ! WVWR7      p\         P                  \         P                  3p\	        Wx4       \        P                  ! WVRWR7      p\        P                  ! W4VVR7      p\	        Wx4       Rp	\
        P                  ! \        V	R7      ;_uu_ 4        \        P                  ! WVRWR7       RRR4       Rp	\
        P                  ! \        V	R7      ;_uu_ 4        \        P                  ! WVR	WR7       RRR4       R#   + '       g   i     LZ; i  + '       g   i     R# ; i)rW   rU  r   )r   r  r  r   r   r   Nr   ra  r  rw   rz   rJ   rF   rI   )r   rb   r[   rw  r
   r   r   r   )
rc   r  r  r  r  rf  rg  rh  ri  r  s
   &&&       rm   r  )TestKendallTauAlternative.test_nan_policy  s    bffXbffX %%e-3N
'
1 %%ev-3N
''v4?A
1 2]]:W55Ug$*E 6
 1]]:W55Uk$*E 65 65 655s   E'EE	E/	r   N)r  r  r  )rW   rW   r1   )rW   RUUUU?ZUUUU?)g~?r  r  )?rW   r  )ˮ[?rW   r  )g?gSǌ?gSǌ?)g:
?g3
?g<t'.?)gN  A?gss?gYss?)r  r  rn  )/r   r   r   r   r  alternativesr   rb   p_n1p_n2p_c0p_c1p_no_correlationp_no_correlationb
p_n_lt_171p_n_lt_171bp_n_lt_171cr  r:  r5  reversed	case_R_n1r   r   r  r  	case_R_n2r  	case_R_c0r  	case_R_c1r  case_R_no_corrr  case_no_cor_br  case_R_lt_171r  case_R_lt_171br  case_R_lt_171cr  case_gt_171r  r  r   r   r   s   @rm   r  r    s    '>h 4LFFBFFBFF#DD0D>D<=DJCKGK+ c,ugai89L(4.4&(CDEI [[;YGO HO c,ugai89L(4.4&(CDEI [[;YGK HK
 c,ugai89L(4.4&(CDEI [[;YGK HK
 c,ugai89L(4.4&(CDEI [[;YGK HK
 3|-=wqyIJSx8H/I"&+ ,,N [[;^LK MK
 #l,=wqyIJCh7H.I!%q* ++M [[;]KK LK
 #lJ	BCChz.BTF1HMNOM [[;]KK LK 3|[5'!)DESx/D"&+ ,,N [[;^LK MK 3|[5'!)DESx/D"&+ ,,N [[;^LK MK L5'!)45L4&(345K [[/=	5 >	5 [[X'>?[[],LME N @Erp   r  c                     . ROp . ROp\         P                  ! W4      w  r#\        VR4       \        \        P
                  V4       \         P                  ! WRR7      w  r#\        VR4       \        \        P
                  V4       \         P                  ! WR R7      w  r#\        VR4       \        \        P
                  V4       \         P                  ! W4      pRp\        WE4       \        VP                  VP                  4       \         P                  ! WRR7      w  r#\        VR4       \        \        P
                  V4       \         P                  ! WRR7      w  r#\        VR4       \        \        P
                  V4       \         P                  ! WRRR7      w  r#\        VR4       \        \        P
                  V4       \         P                  ! WRRR7      w  r#\        VR4       \        \        P
                  V4       \         P                  ! WRR7      w  r#\        VR4       \        \        P
                  V4       \         P                  ! WRR	 R
7      w  r#\        VR4       \        \        P
                  V4       \         P                  ! WRR R
7      w  r#\        VR4       \        \        P
                  V4       \         P                  ! \        P                  ! V \        P                  R7      V4      w  r#\        VR4       \         P                  ! \        P                  ! V \        P                  R7      V4      w  r#\        VR4       \         P                  ! \        P                  ! V \        P                  R7      \        P                  ! V\        P                  R7      4      w  r#\        VR4       \        P                  ! \        RR7      ;_uu_ 4        \         P                  ! . . 4      w  r#RRR4       \        \        P
                  V4       \        \        P
                  V4       \        P                  ! \        RR7      ;_uu_ 4        \         P                  ! ^ .^ .4      w  r#RRR4       \        \        P
                  V4       \        \        P
                  V4       \        \         \         P                  ^ ^.. RO4       \        \         \         P                  ^ ^.^ ^.. RO4       . ROp ^^^^\        P
                  .p\         P                  ! W4      w  r#\        VR4       ^^\        P
                  ^^.p \         P                  ! W4      w  r#\        VR4       . R Op RRRR\        P
                  .p\         P                  ! W4      w  r#\        VR4       RR\        P
                  RR.p \         P                  ! W4      w  r#\        VR4       . R!Op . R"Op\         P                  ! W4      w  r#\        VR#4       RR\        P
                  R\        P
                  .p \         P                  ! W4      w  r#\        VR#4       \        P
                  RR\        P
                  \        P
                  .p\         P                  ! W4      w  r#\        VR#4       R#   + '       g   i     EL; i  + '       g   i     ELZ; i)$rQ   F)additivec                     ^# rW   r   rf   s   &rm   <lambda>"test_weightedtau.<locals>.<lambda>  s    Qrp   )weigherN)rank)r  r  Tc                     ^# r  r   r  s   &rm   r  r        rp   )r  r  c                     ^# r  r   r  s   &rm   r  r    r  rp   r6   rp  r         (@r   r   r   r   rt  ru  gs$gROorv  r<  gڿgng @ڿg[đ(gIکn࿩ry   rW   rE   )r  r   r   r  r   )r  r   r   r  r   )r   r   r   r   r   gt34+)r[   weightedtaur	   r   r   rb   r   r;  r>  rY   r   r   r   rb  r   r   r   )rf   rg   r~  r  r   r@  s         rm   test_weightedtaur    s   AA$$Q*LC12!$$QE:LC12!$$Q;?LC12! 

A
!C*J(#--0 $$Q5LC01!$$Q5LC01!$$QuELC12!$$QuELC12!$$Q6LC12!$$QkJLC12!$$QkJLC12!$$RZZ%DaHLC12$$RZZ%BAFLC12$$RZZ%D%'ZZ%DFLC12	(0G	H	H((R0 
I!	(0G	H	H((!qc2 
I!*e//!QC*e//!Q!QKA	
Aq!RVVA$$Q*LC12	QAA$$Q*LC12#A	c3RVV$A$$Q*LC12	sBFFD#&A$$Q*LC12#A!A$$Q*LC01	sBFFD"&&)A$$Q*LC01	c266266*A$$Q*LC01K 
I	H	H 
I	H	Hs   4[.[[	[,	c                  >   R p \         P                  ! \        V R7      ;_uu_ 4        \        P                  ! ^.R.4       \        P                  ! ^.R.4       \        P                  ! \
        P                  .^4.4       RRR4       R#   + '       g   i     R# ; i)z)One or more sample arguments is too smallr   r   N)r   rb  r   r[   r  r   rb   )r  s    rm   test_segfault_issue_9710r  #  sj     :G	(	8	81#u%1#u%266(RD)	 
9	8	8	8s   ABB	c                  >   ^p \         P                  ! V ^,           4      P                  \        4      p\         P                  ! V ^,           4      P                  \        4      p\         P                  VR&   \
        P                  ! WRRR7      w  r4\        VR4       R# )   r  r   )r  r   r   NrU   )r   r   r  r  rb   r[   rw  r   )r  rf   rg   _r  s        rm   test_kendall_tau_larger  /  sn    A
		!a%&A
		!a%&AFFAbEqGGGAsrp   c            
      <   R  p R p\         P                  P                  ^*4      p\        ^^
4       F  p. p\        V4       F  pWE.V,          ,          pK  	  \	        V4      pVP                  V4       VP                  V4       \         P                  ! \        V4      \         P                  R7      p\        ^4       FT  pR F:  p	V ! WFWqV	4      p
\        P                  ! WFWqV	4      P                  p\        W4       K<  	  VP                  V4       KV  	  K  	  R# )c                    ^ ;p;p;p;r\        \        \        V 4      4      \        \        V 4      4      4       EF>  w  rV'       d"   V! W*,          4      V! W+,          4      ,           M V! W*,          4      V! W+,          4      ,          pW\,          pW
,          W,          8X  d	   W,          pW,          W,          8X  d	   W,          p	W
,          W,          8  d   W,          W,          8  g'   W
,          W,          8  d   W,          W,          8  d   Wl,          pK  W
,          W,          8  d   W,          W,          8  g-   W
,          W,          8  g   EK   W,          W,          8  g   EK6  W|,          pEKA  	  Wg,
          \        P                  ! WX,
          4      ,          \        P                  ! WY,
          4      ,          # ry   )r   r  lenr   rH  )rf   rg   r  r  addtotconcdiscuvr  r  ws   &&&&&        rm   wkq*test_weightedtau_vs_quadratic.<locals>.wkq;  s$   $%%%d%T%AeCFmU3q6];FQ7: 747#33TW%(88 HCtqt|tqt|tad{qtad{adQTkadQTk	qtqt	 < rwwsw//"''#'2BBBrp   c                 "    R V ^,           ,          # )r   r   r  s   &rm   r  .test_weightedtau_vs_quadratic.<locals>.weigherK  s    QU|rp   r6   NrS   )r   r  r  r  r:  r  r   r   intpr[   r  r>  r	   )r  r  r  r  rK  r  rW  r  r  r  r  r  s               rm   test_weightedtau_vs_quadraticr  9  s    C  ))


#C1R[qAQJA GAAyyQrww/qA$qTC8**1DNN#H5 %
 KK  rp   c                   ,   a  ] tR tRt o R tR tRtV tR# )TestFindRepeatsib  c                    . ROpRp\         P                  ! VR7      ;_uu_ 4        \        P                  ! V4      w  r4RRR4       \	        X. RO4       \	        X. RO4       R#   + '       g   i     L.; i)rW   +`scipy.stats.find_repeats` is deprecated...r   N)rW   rE   r   r   rW   rE   r   r   rW   rE   rw   r  )r   r   rE   rE   r   deprecated_callr[   find_repeatsr   )rc   rK  r  r   numss   &    rm   rX  TestFindRepeats.test_basicd  sQ    -?##'22**1-IC 33-4. 32s   A%%A5	c                    . RO. 3 F]  pRp\         P                  ! VR7      ;_uu_ 4        \        P                  ! V4      w  r4RRR4       \	        X. 4       \	        X. 4       K_  	  R#   + '       g   i     L.; i)rO   r  r   N)rO      2      (   r  )rc   rK  r  repeatedcountss   &    rm   test_empty_result!TestFindRepeats.test_empty_resultl  sZ    &+ACG''g66#(#5#5a#8  7x,vr* ,66s   A**A:r   N)r   r   r   r   rX  r  r   r   r   s   @rm   r  r  b  s     /+ +rp   r  c                      a  ] tR tRt o R tR tR tR tR tR t	R t
R	 tR
 tR tR tR tR tR tR tR tRtV tR# )TestRegressioniv  c                    \         P                  ! \        \        4      p\	        VP
                  R 4       \	        VP                  R4       \	        VP                  R4       \	        VP                  R4       R# )ir   r   N)	r[   
linregressrZ   r   r   	interceptrvaluestderrintercept_stderrrc   r  s   & rm   test_linregressBIGX"TestRegression.test_linregressBIGXw  sR    !!!S)F,,h7FMM3/ 	FMM3/F33S9rp   c                    \         P                  ! \        \        4      p\        VP                  R 4       \        VP
                  R4       \        VP                  R 4       \        VP                  R 4       R# )r   r   N)r[   r#  rZ   r   r$  r%  r&  r'  r(  s   & rm   test_regressXXTestRegression.test_regressXX  sR    
 !!!Q'F,,c2FMM3/FMM3/F33S9rp   c                   \         P                  ! \        \        4      p\	        VP
                  R 4       \        P                  ! \         P                  RR7      ;_uu_ 4        \         P                  ! \        \        4      P                  pRRR4       \	        VP                  X4       R#   + '       g   i     L(; i)r   zAn input array...r   N)r[   r#  rZ   ZEROr   r$  r   rb  rc  r   r>  r%  )rc   r  
ref_rvalues   &  rm   test_regressZEROX TestRegression.test_regressZEROX  sr    
 !!!T*F,,c2\\%44<OPP40::J QFMM:6 QPs   $*B..B>	c                t   \         P                  ! ^ ^d^d4      pR\         P                  ! ^ ^d^d4      ,          ^
,           pV\         P                  ! \         P                  ! ^ ^^d4      4      ,          p\        P                  ! W4      p\
        p\        \        W44      4       \        VP                  R4       R# )ry   皙?g4_Qc?N)
r   linspacesinr[   r#  r    r   
isinstancer   r&  )rc   rf   rg   r  lrs   &    rm   test_regress_simple"TestRegression.test_regress_simple  s    KK3$"++ac**R/	RVVBKK2s+,,!!!'
6&'FMM+@Arp   c                6   \         P                  ! ^ ^d^d4      pR\         P                  ! ^ ^d^d4      ,          ^
,           pV\         P                  ! \         P                  ! ^ ^^d4      4      ,          p\        P                  ! \
        RR7      ;_uu_ 4        \        P                  ! WRR7       RRR4       \        P                  ! WRR7      p\        P                  ! WRR7      p\        VP                  ^VP                  ^,          ,
          4       \        P                  ! WR	R7      p\        VP                  VP                  ^,          4       VP                  VP                  u;8X  d   VP                  8X  g   Q h Q hR#   + '       g   i     L; i)
ry   r4  r`  r   ra  r  Nr  r  r  )r   r5  r6  r   r   r   r[   r#  r
   r=  r%  )rc   rf   rg   r  r  r  s   &     rm   test_regress_alternative'TestRegression.test_regress_alternative  s   KK3$"++ac**R/	RVVBKK2s+,,]]:-NOOQ{; P +> &9Q$++/%:; )<T[[1_5{{dkk8T[[88888 POs   FF	c                v   . R	Op. R
Op\         P                  ! WRR7      p\        VP                  R4       \        VP                  R4       \        VP
                  \        P                  ! R4      4       \        VP                  R4       \        VP                  R4       \        VP                  R4       R# )   r  r  gؗh?gag?g->g5ՒO?g]؊E @N)
r?                             )
?   Q   8   [   /   9   r3  H   >   0   gJK@:C)r[   r#  r
   sloper$  r%  r   rH  r=  r&  r'  )rc   rf   rg   r   s   &   rm   test_regress_against_R%TestRegression.test_regress_against_R  s     ?4q=		?3'89

BGGM$:;

$56

O4,,o>rp   c                   \         P                  ! ^4      p\         P                  ! ^^4      pV^R	.;;,          ^,          uu&   V^ R
.;;,          ^,          uu&   \        P                  ! W4      pR pV! VP                  R4       V! VP
                  R4       V! VP                  R4       V! VP                  R4       V! VP                  R4       V! VP                  R4       R# )rP   c                     \        W^R7      # )rM   r  )r   )rf   rg   s   &&rm   	assert_ae1TestRegression.test_linregress.<locals>.assert_ae  s    &qR88rp   r   r8   gePUn?g.bt>gڽE?gʺL7?NrU   )
r   r   r[   r#  rR  r$  r%  r=  r&  r'  )rc   rf   rg   r  rX  s   &    rm   test_linregressTestRegression.test_linregress  s    IIbMIIa	A+!	A+!!!!'	9&,,$&""C(&--!12&--1&--!56&))+>?rp   c                   R Rr!\         P                  ! V^V,          V4      p\         P                  ! ^V,          W4      p\        P                  ! W44      p\	        VP
                  R8  4       \        VP
                  R4       \	        \         P                  ! VP                  4      '       * 4       \	        \         P                  ! VP                  4      '       * 4       R# )gJr 11順 NrU   )
r   r5  r[   r#  r   r%  r   rw  r&  r'  )rc   rK  r  rf   rg   r  s   &     rm    test_regress_simple_negative_cor/TestRegression.test_regress_simple_negative_cor  s     f1KK1q5!$KKAq$!!!' 	#$FMM2. 	BHHV]]++,BHHV44556rp   c                   \         P                  ! ^ ^d^d4      pR\         P                  ! ^ ^d^d4      ,          ^
,           pV\         P                  ! \         P                  ! ^ ^^d4      4      ,          p\        P                  ! W4      p\
        p\        \        W44      4       Rp\        W54       R\        V4      9   g   Q hR# )ry   r4  r'  N)rR  r$  r%  r=  r&  )
r   r5  r6  r[   r#  r    r   r7  r   dir)rc   rf   rg   r  r8  r@  s   &     rm   !test_linregress_result_attributes0TestRegression.test_linregress_result_attributes  s    KK3$"++ac**R/	RVVBKK2s+,,!!!' 
6&' J
F/!S[000rp   c                   \         P                  ! ^4      p\         P                  ! ^^4      p\        P                  ! W4      p\	        VP
                  R4       \	        VP                  R4       \	        VP                  R4       R# )rE   r   N)r   r   r[   r#  r   r=  r&  r'  rc   rf   rg   r  s   &   rm   test_regress_two_inputs&TestRegression.test_regress_two_inputs	  s^    IIaLIIaO!!!' 	FMM3/ 	FMM3/F33S9rp   c                   \         P                  ! ^4      p\         P                  ! ^4      p\        P                  ! W4      p\        VP                  R4       \        VP                  R4       \        VP                  R4       R# )rE   r   r   N)	r   r   r  r[   r#  r   r=  r&  r'  rf  s   &   rm   'test_regress_two_inputs_horizontal_line6TestRegression.test_regress_two_inputs_horizontal_line	  s\    IIaLGGAJ!!!' 	FMM3/ 	FMM3/F33S9rp   c                p   . R NRNRNRNRNRNRNRNRNR	NR
NRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNR NR!NR"Np. R#NR$NR%NR&NR'NRNR(NR)NR*NR+NR,NRNR#NR-NR.NR/NR!NR0NR1NR2NR3NR4NR5NRNRNR6NR/NR&NR)NR+NR7NR8NR9NR:NR;NR Np\         P                  ! W4      p\        VP                  R<4       \        VP                  RB4       \        VP
                  ^,          R=4       \        VP                  R>4       \        VP                  R?4       \        VP                  R@4       RA# )Cr4  gfffffu@ǧ]@g̤@333333$@g     Pl@gfffff҄@gfffff"@g	|@g     H@gq@皙?333333?g     <@g33333ׄ@g      u@g     {@g333333'@g     `@g33333l@gfffff@g̼@g^@rG  gffffff@g1u@g@g     8@g     X@333333&@g33333]@gfffffl@g@gfffff|@r1   rD  g,u@gfffff]@g     @r  g     @g     4@g|@g33333W@gy@gP@gfffff@g4u@g%@gm@gl@g     0@gfffffƋ@gfffff]@gl@gffffff$@gffffff]@g̜l@g33333@g33333|@g?gpX?r   gh-h*<?gg?Ng!п)	r[   r#  r   rR  r$  r%  r=  r&  r'  rf  s   &   rm   test_nist_norrisTestRegression.test_nist_norris&	  s    7s 7E 75 7% 7 7 777 7"'7).725777 7"'7).7157 7 7 !7 #(7 */7 367 	7 	7 !	7 #(	7 */	7 16	7
 7
 7
 !7
 #(7
 */7
 3677s 7E 75 7% 7 7 777 7"'7).725777 7"'7).7157 7 7 !7 #(7 */7 367 	7 	7 !	7 #(	7 */	7 16	7
 7
 7
 !7
 #(7
 */7
 367 !!!'FLL*:;F,,.@AFMM1,.?@FMM3/FMM+;<F335EFrp   c                   \         P                  ! ^ ^d^d4      pR\         P                  ! ^ ^d^d4      ,          ^
,           pV\         P                  ! \         P                  ! ^ ^^d4      4      ,          p\        P                  ! W4      p\         P
                  ! W^4      p\        VP                  V^ ,          4       \        VP                  V^,          4       R# )ry   r4  N)	r   r5  r6  r[   r#  polyfitr   rR  r$  )rc   rf   rg   r  polys   &    rm   test_compare_to_polyfit&TestRegression.test_compare_to_polyfitA	  s    KK3$"++ac**R/	RVVBKK2s+,,!!!'zz!" 	FLL$q'2F,,d1g6rp   c                   \         P                  ! \        R R7      ;_uu_ 4        \        P                  ! . . 4      p\
        P                  ! \
        P                  ! V4      4      '       g   Q h RRR4       R#   + '       g   i     R# ; i)rp  r   N)r   rb  r   r[   r#  r   r  rw  rc   r   s   & rm   test_empty_inputTestRegression.test_empty_inputM	  sT    \\,4KLL""2r*C66"((3-(((( MLLLs   A
A::B	c                   \         P                  ! R 4      p\         P                  V^	&   \         P                  ! RR7      ;_uu_ 4        \        P
                  ! W4      pRRR4       \        p\        \        XV4      4       \        V\         P                  3^,          4       \        VP                  \         P                  4       R#   + '       g   i     Ls; i)r   ignoreinvalidN)r   r   rb   errstater[   r#  r    r   r7  r   r   r'  )rc   rf   r  r8  s   &   rm   test_nan_inputTestRegression.test_nan_inputR	  s    IIcNvv![[**%%a+F + 
62&'6BFF9Q;/V,,bff5 +*s   	CC	c                   \         P                  ! ^
4      p\         P                  P                  ^
4      pRp\        \        VR7      ;_uu_ 4        \
        P                  ! W4       RRR4       R#   + '       g   i     R# ; i)rO   z$Cannot calculate a linear regressionr   N)r   rY  r  r   r   r[   r#  rc   rf   rg   r   s   &   rm   test_identical_xTestRegression.test_identical_x_	  sR    HHRLIIR 4:S11Q" 2111s   A22B	r   N)r   r   r   r   r)  r,  r1  r9  r<  rS  r[  r_  rc  rg  rj  rq  rv  rz  r  r  r   r   r   s   @rm   r!  r!  v  s]     :
:*	7	B9*?&@,7$1 ::G6
7)
6# #rp   r!  c                     \         P                  ! . RO4      w  rr#\        V R4       \        VR4       Rp\        P                  ! \
        VR7      ;_uu_ 4        \         P                  ! . RORR7       RRR4       \         P                  ! . RORR7      w  rr#\        V R4       \        VR4       . ROp. ROp\         P                  ! WeR	R
R7      w  rr#\        V ^4       \        VR4       \        VR^R7       \        VR^R7       \         P                  ! WeR	RR7      w  rr#\        V ^4       \        VR4       \        VR^R7       \        VR^R7       R#   + '       g   i     L; i)ry   r1   zHmethod must be either 'joint' or 'separate'.'joint_separate' is invalid.r   joint_separater  Njointr   gQ?separater   gQ@rW  gGz@r   ry   rW   rW   )rW   rE   r   r   rO   rQ      )rI         r  -   7   N   )r[   theilslopesr   r   r   r   )rR  r$  lowerupperr   rf   rg   s          rm   test_theilslopesr  g	  s1   %*%6%6w%?"Ees#	3'*C	z	-	-),<= 
. &+%6%6y>E&G"Ees#	3' 	!A#A%*%6%6qT>H&J"Eeq!	3'tQ/tQ/%*%6%6qT>E&G"Eeq!	3'tQ/tQ// 
.	-s   EE,	c                  (   . ROp \         P                  ! V ^R7      w  rr4\        V\        P                  ! . RO4      4       \         P                  ! V ^RR7      w  rr4\        V^8H  4       Rp\         P                  ! V ^RR7      p\        We4       R# )rW   numbins)r  defaultreallimitsNrW   r   rE   rW   r   rW   )r   r   r8   r   )r2   rw   )cumcountr   binsizeextrapoints)r[   cumfreqr   r   r   r   r   )rf   cumfreqslowlimr  r  r@  r   s          rm   test_cumfreqr  	  sy    A-2]]1a-H*Hgh1A(BC-2]]	1.2*HgK1 FJ
--1
AC(rp   c                  4   \         P                  ! . RO4      p \        P                  ! V ^R7      w  rr4\	        V\        . RO4      4       Rp\        P                  ! V ^R7      p\        We4       \        P                  ! . RO^R7      w  rrr4\	        W4       R# )rW   r  Nr  )r1   K}\UU?r  r  )	frequencyr   r  r  )r   r   r[   relfreqr   r   )rK  relfreqsr  r  r  r@  r   	relfreqs2s           rm   test_relfreqr  	  s~    
#$A-2]]1a-H*Hgh#$MNP GJ
--1
%C( /4mm<NDE/G+Iwh2rp   c                   P   a  ] tR tRt o R tR tR tR tR tR t	R t
R	 tR
tV tR# )TestScoreatpercentilei	  c                <    . ROV n         . ROV n        . ROV n        R# )r   N)r   r   rw   rO   rV   rz   )r   rZ  rF   rJ   r   rE   rW   )r   r   rw   rO   rV   r  r  r   a1a2a3r|  s   &rm   setup_method"TestScoreatpercentile.setup_method	  s    *,1rp   c                    \        ^4      R,          p\        \        P                  ! V^ 4      R4       \        \        P                  ! V^d4      R4       \        \        P                  ! V^24      R4       R# )rF   r1   r         @      ?N)r   r   r[   scoreatpercentiler  s   & rm   rX   TestScoreatpercentile.test_basic	  sT    1IOU,,Q2B7U,,Q4c:U,,Q3T:rp   c           	     P   \         P                  p\        V! \        \	        ^
4      4      ^24      R4       \        V! \        \	        ^
4      4      ^2R4      R4       \        V! \        \	        ^d4      4      ^2R	R7      R4       \        V! \
        P                  ! . R
O4      ^2R4      ^74       \        V! \
        P                  ! . R
O4      ^2R4      R4       \        V! \        \	        ^
4      4      ^2RR7      R4       \        V! \        \	        ^
4      4      ^2RRR7      R4       \        V! \        \	        ^d4      4      ^2R	RR7      R4       \        V! \
        P                  ! . R
O4      ^2RRR7      ^74       \        V! \
        P                  ! . R
O4      ^2RRR7      R4       R# )rO   rA   )limitrB   fractioninterpolation_methodr  r  NrE   rJ   rW   rF   rW   rO   r  rO   r  rW   rO   r[   r  r   r:  r  r   r   rc   scoreatpercs   & rm   test_fraction#TestScoreatpercentile.test_fraction	  sP   -- 	[eBi"5s;[eBi"e<cB[eCj!12VDcJ[+!6HErJ[+!6FCSI 	[eBi":V	[eBi"F6@B	 	[eCj!12V6@B	 	[+!6I6@B	 	[+!6F6@B	rp   c           	     b   \         P                  p\        V! \        \	        ^
4      4      ^2RR7      ^4       \        V! \        \	        ^
4      4      ^2RR7      ^4       \        V! \        \	        ^
4      4      ^2RRR7      ^4       \        V! \        \	        ^
4      4      ^2RRR7      ^4       \        V! \        \	        ^d4      4      ^2RRR7      ^4       \        V! \        \	        ^d4      4      ^2RRR7      ^4       \        V! \
        P                  ! . RO4      ^2R	RR7      ^
4       \        V! \
        P                  ! . RO4      ^2R	RR7      ^d4       \        V! \
        P                  ! . RO4      ^2R
RR7      ^4       \        V! \
        P                  ! . RO4      ^2R
RR7      ^
4       R# )rO   r  r  higherr  Nr  r  r  r  r  r  r  s   & rm   test_lower_higher'TestScoreatpercentile.test_lower_higher	  s~   -- 	[eBi"6=?@A	C[eBi"6>@AB	D[eBi"e6=?@A	C[eBi"E6>@AB	D[eCj!12u6=?@A	C[eCj!12u6>@AB	D[,!7Y6=?@B	D[,!796>@AD	F[,!7W6=?@A	C[,!776>@AC	Erp   c           	     >   \        ^4      R,          p\        P                  ! . RO4      p\        P                  ! V. RO4      p\        W24       \        \        V\        P                  4      4       \        \        P                  ! V\        P                  ! . RO4      4      V4       \        P                  ! \        P                   ! ^4      P                  R4      \        P                  ! . RO4      ^R7      p\        . RO. R	O. R
O. R
O.4      p\        WE4       R# )rF   r1   r>   N)ry   r  r  )ry   r  r  r   r   )ry   rW   r  r  )ry   r   rF   )Q?gQ@g(\ @r   rJ   rP   )
r   r   r   r[   r  r
   r   r7  ndarrayr]   )rc   rf   r  r   r  	expected2s   &     rm   test_sequence_per'TestScoreatpercentile.test_sequence_per	  s    1IO88N+%%a6&
3

+,//288L3IJ 	" &&ryy}'<'<U'C')xx0@'AK9-%%' (	 	(rp   c                &   \         P                  p\        ^4      P                  ^^4      p\	        V! VR4      . RO4       . RO. RO. RO.p\	        V! VR^ R7      V4       . R	O. R
O. RO.p\	        V! VR^R7      V4       \        . RO. RO. RO. RO. RO.4      p\         P                  ! V^24      p\	        VP                  R4       \	        VR4       \         P                  ! V^2^ R7      p\	        VP                  R4       \	        V. RO4       R# )rQ   r>   r   N)   r  r  )g      @rB         &@)rE   r   r   rw   r   rw   rz   rJ   )rF   rI   rO   rP   )      ?g      @g     !@)r2   rB         #@r  rW   rW   rW   )r   r   r   r   r   )r[   r  r   r]   r   r   r  )rc   r  rf   r0r  scores   &     rm   	test_axisTestScoreatpercentile.test_axis	  s    --2Jq!$[M24EFL.9[M:B? /:>[M:B?9	 
 ''2.U[["%UC ''2A6U[[$'UI&rp   c                    \        \        \        P                  ^^.^8RR7       \        \        \        P                  ^.^e4       \        \        \        P                  ^.R4       R# )rW   r   r  NrU   )r   r   r[   r  r|  s   &rm   test_exception$TestScoreatpercentile.test_exception
  sK    j%"9"9Aq62+3	5j%"9"9A3Dj%"9"9A3Crp   c                p   \        \        P                  ! . ^24      \        P                  4       \        \        P                  ! \        P
                  ! . . .4      ^24      \        P                  4       \        \        P                  ! . ^2^c.4      \        P                  \        P                  .4       R# )r  N)r   r[   r  r   rb   r   r|  s   &rm   
test_empty TestScoreatpercentile.test_empty
  sm    U,,R4bff=U,,RXXr2h-?DbffMU,,R"b:RVVRVV<LMrp   r  N)r   r   r   r   r  rX  r  r  r  r  r  r  r   r   r   s   @rm   r  r  	  s6     2
;4E2)$'0DN Nrp   r  c            
          a  ] tR tRt o R tR tR tR t]P                  P                  R]P                  ! R^ 4      4      R 4       tR tR	 t]P                  P                  R
. RO^]P                   ^^^^.. RO^]P                   ^^..4      ]P                  P                  RRR.4      R 4       4       t]P                  P                  R]P                  ! R ^4      4      ]P$                  3R l4       tR tR t]P                  P                  RRR.4      R 4       tR t]P                  P1                  R4      ]P                  P                  R]P2                  ! R!4      ]P2                  ! R"4      .4      R 4       4       tR tRtV tR# )#TestModei
  c                >   \         P                  ! \        \        R 7      ;_uu_ 4        \        P
                  ! . 4      w  rRRR4       \        X\        P                  ! . 4      4       \        X\        P                  ! . 4      4       R#   + '       g   i     LR; ir   N)	r   rb  r   r   r[   moder   r   r   rc   valsr  s   &  rm   r  TestMode.test_empty
  sX    \\,4IJJ ::b>LD KT288B<(VRXXb\* KJs   BB	c                    \         P                  ! R 4      w  r\        V\        P                  ! R .4      4       \        V\        P                  ! ^.4      4       R# )r   N)r[   r  r   r   r   r  s   &  rm   rx  TestMode.test_scalar%
  s9    zz"~T288RD>*VRXXqc]+rp   c                    . ROp\         P                  ! V4      p\        V^ ,          ^4       \        V^,          ^4       R# )r   Nr   rw   rW   rO      r   rE   rz   rF   rz   rO   rz   r[   r  r   )rc   data1r  s   &  rm   rX  TestMode.test_basic*
  s1    7zz% T!Wa T!Wa rp   c           
        . ROp. ROp. ROp. ROp. ROp\         P                  ! WW4V.4      p\        P                  ! VRRR7      p\	        V^ ,          \         P                  ! ^..4      4       \	        V^,          \         P                  ! ^..4      4       \        P                  ! V^ RR7      p\	        V^ ,          \         P                  ! . R	O.4      4       \	        V^,          \         P                  ! . R
O.4      4       \        P                  ! V^RR7      p\	        V^ ,          \         P                  ! ^
.^
.^.^.^..4      4       \	        V^,          \         P                  ! ^.^.^.^.^..4      4       R# )rO   NTr?   keepdims)rO   rO   r  r  )rO   rO   rO   rO   )r  rO   r  r  )r  r  r  r  )r  r  r  r  )rO   rO   r  r  )rE   r   r   rE   )r   r   r[   r  r   )rc   r  data2data3data4data5arrr  s   &       rm   	test_axesTestMode.test_axes0
  s'        hheE:;zz#D48T!Wbhhv./T!Wbhhuo.zz#A5T!Wbhh(8'9:;T!Wbhh~67zz#A5T!WbhhrdRD2$'EFGT!WbhhaS1#sQC'@ABrp   r?   c                D   \         P                  P                  R 4       \         P                  P                  ^
^^^4      p\        P
                  ! W"P                  V,           R7      p\        P
                  ! W!R7      p\         P                  P                  W44       R# ):r>   N)	r   r  r  r  r[   r  ndimr"  r   )rc   r?   rK  r  r  s   &&   rm   test_negative_axes_gh_15375$TestMode.test_negative_axes_gh_15375D
  s`    
		y!IINN2r2r*zz!&&+.zz!'


%%d1rp   c                $   . ROp. p\         P                  ! V4      pRp\        W44       \        P                  ! \
        \        R7      ;_uu_ 4        \         P                  ! V4      pRRR4       \        XV4       R#   + '       g   i     L; i)r   r   Nr  )r  count)r[   r  r   r   rb  r   r   )rc   r  r  r  r@  actual2s   &     rm   test_mode_result_attributes$TestMode.test_mode_result_attributesL
  sb    7E"&
F/\\,4IJJjj'G KGZ0 KJs   A??B	c                P   ^\         P                  ^^^
^^^^^^^
^.p\        P                  ! V4      p\	        VR4       \        P                  ! VRR7      p\	        VR4       \        \        \        P                  VRR7       \        \        \        P                  VRR7       R# )r   r   r   r   r   N)rz   r   )r   rb   r[   r  r   r   r   )rc   r  r  s   &  rm   test_mode_nanTestMode.test_mode_nanV
  s|    BFFAq"b!Q1aQ?E"VV$Ef5VV$j%**eHj%**eIrp   datar  FTc                    \         P                  ! VR VR7      pV'       d   \        V^ ,          ^ ,          ^4       R# \        V^ ,          ^4       R# )r   )r   r  Nr  )rc   r  r  r  s   &&& rm   test_smallest_equalTestMode.test_smallest_equal`
  s9     DVhG1q)A&rp   c                   \         P                  P                  R 4      pVP                  RR7      P	                  V4      p\
        P                  ! WARR7      p\        VP                  4      pVP                  V4       \         P                  P                  VP                  P                  V4       \         P                  P                  VP                  P                  V4       R# )r  r  Fr  Nr   r   rw   )r   r  r  uniformr  r[   r  r:  r  popr"  r   r  )rc   r?   r7   r  rK  r   reference_shapes   &&&    rm   test_mode_shape_gh_9955 TestMode.test_mode_shape_gh_9955n
  s    ii##I.KKYK'..u5jj6qww-D!


%%chhnnoF


%%ciiooGrp   c                    ^\         P                  ^\         P                  .p\        P                  ! V4      p\         P                  ! VP                  4      '       d   VP
                  ^8X  g   Q hR# rE   N)r   rb   r[   r  rw  r  )rc   rK  r   s   &  rm   !test_nan_policy_propagate_gh_9815*TestMode.test_nan_policy_propagate_gh_9815x
  sL     266"jjmxx!!cii1n44nrp   c                ~   \         P                  ! R	4      p\        P                  ! V^RR7      pVP                  P                  VP
                  P                  u;8X  d	   R
8X  g   Q h Q h\        P                  ! V^RR7      pVP                  P                  VP
                  P                  u;8X  d	   R8X  g   Q h Q h^^^\         P                  .^^\         P                  ^..p\        P                  ! V^RR7      p\        VP                  ^^.4       \        VP
                  ^^.4       \        P                  ! V^RR7      p\        VP                  ^.^..4       \        VP
                  ^.^..4       \         P                  ! V4      p\        P                  ! VRRR7      p\        P                  ! VP                  4       RR7      p\        W#4       VP                  P                  VP                  P                  u;8X  d	   R8X  g   Q h Q h\        P                  ! VRRR7      p\        P                  ! VP                  4       RR7      p\        VP                  P                  4       VP                  P                  4       4       VP                  P                  R8X  g   Q h\        VP
                  P                  4       VP
                  P                  4       4       VP
                  P                  R8X  g   Q h^\         P                  \         P                  \         P                  ^.\         P                  \         P                  \         P                  \         P                  ^.^^\         P                  ^^..p\        P                  ! V^RRR7      p\        VP                  . RO4       \        VP
                  . RO4       \        P                  ! V^RRR7      p\        VP                  ^.^.^..4       \        VP
                  ^.^.^..4       \         P                  ! V4      p\        P                  ! VRRRR7      p\        P                  ! VP                  4       RRR7      p\        W#4       VP                  P                  VP                  P                  u;8X  d	   R8X  g   Q h Q h\        P                  ! VRRRR7      p\        P                  ! VP                  4       RRR7      p\        VP                  P                  4       VP                  P                  4       4       VP                  P                  R8X  g   Q h\        VP
                  P                  4       VP
                  P                  4       4       VP
                  P                  R8X  g   Q hR# )rW   Fr  TNr  r   )r?   r  r   )r  r   )rW   rE   r   ry   )rW   r   ry   )rW   rW   r   ry   r   r  )rW   rE   rw   )rE   rW   rE   )r   rY  r[   r  r  r  rb   r   r   r  r   )rc   rK  r   r  s   &   rm   test_keepdimsTestMode.test_keepdims
  s   HH\"jjU3xx~~=I=====jjT2xx~~@L@@@@@ ArvvArvvq 12jjU3388aV,399q!f-jjT2388qcA3Z0399sQCj1HHQKjj6jjU33$xx~~5255555jj5jjT2SXX^^%sxx~~'78xx~~'''SYY__&		(9:yy&((( +ffbffbffbffa0BFFAq!# jjUvF388Y/399i0jjTfE388qcA3_5399sQC!o6HHQKjj&IjjUvF3$xx~~5255555jjHjjTfESXX^^%sxx~~'78xx~~'''SYY__&		(9:yy&(((rp   r   r  r   c                F   R
p\         P                  ! V4      p\         P                  VR&   \        P                  ! V^RVR7      p\        VP                  . RO4       \        VP                  . RO4       \         P                  ! R\         P                  3R\         P                  R3.4      p\         P                  ! ^
VR7      pRp\        P                  ! \        VR7      ;_uu_ 4        \        P                  ! WaR7       R	R	R	4       R	#   + '       g   i     R	# ; i)r   F)rK  r?   r  r   asdfqwerr6   z=Argument `a` is not....|An argument has dtype...|The DType...r   r   N)r   r   r  rQ  rE   r   r   r   r  )r   r  rb   r[   r  r   r  r7   uint8r   rY  r   r   	TypeError)rc   r   r  r  r   my_dtypetestr  s   &&      rm   test_gh16955TestMode.test_gh16955
  s     wwu~VVT
jj4a%JO388\2399l3 88fbhh/&"**d1KLMxx(+Q]]9G44JJt3 5444s   -DD 	c                   \         P                  ! \        \        R 7      ;_uu_ 4        \        P
                  ! . 4      pRRR4       \        P                  ^ 3p\        XV4       \         P                  ! \        \        R 7      ;_uu_ 4        \        P
                  ! \        P                  .RR7      pRRR4       \        W4       . RO\        P                  \        P                  \        P                  ..p\         P                  ! \        \        R 7      ;_uu_ 4        \        P
                  ! V^RR7      pRRR4       ^\        P                  .^^ .3p\        W4       \        P
                  ! V^RR7      p^\        P                  .^^.3p\        W4       \        P                  ! . . .4      p\         P                  ! \        \        R 7      ;_uu_ 4        \        P
                  ! V^R7      pRRR4       \        P                  \        P                  .^ ^ .3p\        W4       R#   + '       g   i     EL; i  + '       g   i     EL; i  + '       g   i     EL&; i  + '       g   i     L}; i)r   Nr   r   r  r  r>   )r   r2  r2  )r   rb  r   r   r[   r  r   rb   r   r   r   r   r   )rc   r   r  rK  zs   &    rm   test_gh9955TestMode.test_gh9955
  s    \\,4IJJ**R.C KvvqkS#\\,4EFF**bffX&9C GSrvvrvvrvv67\\,4EFF**QQ6:C GBFF|aV$Sjj{;BFF|aV$SHHb"X\\,4IJJ**QQ'C K!Q(S/ KJJ
 GFF
 GFF KJs/   H3(I$I!I/3I	I	I,	/I?	zignore::RuntimeWarningr,  c                   VP                   ^ 8X  dL   \        P                  ! \        \        R7      ;_uu_ 4        \
        P                  ! VRRR7      pRRR4       M\
        P                  ! VRRR7      p\        P                  ! VRRR7      pX^ ,          P                  V^,          P                  u;8X  d   VP                  u;8X  d	   R8X  g   Q h Q hR#   + '       g   i     Ls; i)ry   r   NTr  r  )
r  r   rb  r   r   r[   r  r   r^   r  )rc   r,  r   r  s   &&  rm   test_gh17214TestMode.test_gh17214
  s     66Q;08MNNjj= ON **QTD9CggadT21v||s1v||EsyyEIEEEEE ONs   CC)	c           	        \         '       d   R MRp ! R R4      p\        P                  ! \        VR7      ;_uu_ 4        \        P
                  ! V! \        P                  ! ^4      4      4       RRR4       \        P                  ! \        VR7      ;_uu_ 4        \        P
                  ! \        P                  ! ^\        R7      4       RRR4       R#   + '       g   i     Lo; i  + '       g   i     R# ; i)z'...only boolean and numerical dtypes...z*Argument `a` is not recognized as numeric.c                   0   a  ] tR tRt o R tRR ltRtV tR# )8TestMode.test_raise_non_numeric_gh18254.<locals>.ArrLikei
  c                    Wn         R # r  _xr  s   &&rm   __init__ATestMode.test_raise_non_numeric_gh18254.<locals>.ArrLike.__init__
  s    rp   Nc                @    V P                   P                  \        4      # r  )r7  r  object)rc   r7   r@   s   &&&rm   	__array__BTestMode.test_raise_non_numeric_gh18254.<locals>.ArrLike.__array__
  s    ww~~f--rp   r6  )NN)r   r   r   r   r8  r<  r   r   r   s   @rm   ArrLiker4  
  s     . .rp   r>  r   Nr6   )	r-   r   r   r&  r[   r  r   r   r;  )rc   r  r>  s   &  rm   test_raise_non_numeric_gh18254'TestMode.test_raise_non_numeric_gh18254
  s    @O<D 		. 	. ]]9G44JJwryy|,- 5]]9G44JJryy&12 54 54444s   1C1C*C'	*C;	r   N)r   rw   rW   rW   r   )r   rw   rW   rV   r  r+  )r   r   r   r   r  rx  rX  r  r   r   r  r   r   r  r	  r  rb   r  r   r  r  r  r)  r-  r   emptyr0  r?  r   r   r   s   @rm   r  r  
  s    +,
!C( [[VRYYr1%562 721J [[V	
BFFAq!Q	
BFFAq	&  [[Z%7' 8' [[VRYYr1%5624** H 7H5:)x [[\K+@A4 B4": [[ 89[[S288I#68K"LMF N :F3 3rp   r  c                      a  ] tR tRt o . ROtRt]P                  P                  R4      R 4       t	R t
]! RRR7      R	 4       tR
tV tR# )TestSEMi  r   r  c                X   VP                  V P                  4      R,          p\        V4      '       dI   \        P                  ! \
        \        R 7      ;_uu_ 4        \        P                  ! V4      pRRR4       Mo\        P                  P                  4       ;_uu_ 4       pVP                  \        4       VP                  \        4       \        P                  ! V4      pRRR4       VP                  X4      '       g   Q hR#   + '       g   i     L+; i  + '       g   i     L>; ir   Nr   )rY   scalar_testcaser)   r   rb  r   r   r[   semr   r"  r   r   UserWarningr   rw  )rc   rd   rG  rg   r   s   &&   rm   test_sem_scalarTestSEM.test_sem_scalar  s     **T%9%9:2>B<<08MNNIIo. ON --//3

;'

>*IIo. 0 xx{{{ ON 0/s   D"ADD	D)	c                @   VP                  V P                  4      p\        P                  ! V4      p\	        W1P                  R 4      4       \        V P                  4      p\	        \        P                  ! V^ R7      WD^,
          ,          R,          ,          \        P                  ! V^R7      4       VP                  R4      pVP                  V^	8H  VP                  V4      p\        \        P                  ! V4      VP                  VP                  4      4       R# )g㝎?ddofr1   r   N)
rY   testcaser[   rH  r/   r   r   whererb   r0   )rc   rd   rO  rg   r  rf   s   &&    rm   test_semTestSEM.test_sem  s    ::dmm,IIh::l34		(3qA#wnD		(3	5 IIcNHHQ!VRVVQ'		!bjj&89rp   Tz(`nan_policy` only supports NumPy backendr   c                    \         P                  ! R 4      p\         P                  V^	&   \        \        P
                  ! VRR7      R4       \        \        \        P
                  VRR7       \        \        \        P
                  VRR7       R# )r   r   r   gH=6?r   r   N)r   r   rb   r   r[   rH  r   r   r   s   && rm   test_sem_nan_policyTestSEM.test_sem_nan_policy+  sX     IIcNvv!UYYqV46HIj%))Q7Cj%))Q8Drp   r   NrD  )r   r   r   r   rO  rG  r   r   r   rJ  rQ  r   rT  r   r   r   s   @rm   rD  rD    s[       HO[[ LM N$
: dGIEIErp   rD  c                     a  ] tR tRt o ]P
                  P                  R. RO. RO3. RO. RO3.4      R 4       tR tR t	]P
                  P                  R^ ^.4      R 4       t
]P
                  P                  R^ ^.4      R 4       t]! R	R
R7      R 4       t]P
                  P                  R4      ]P
                  P                  R4      R 4       4       t]P
                  P                  R4      R 4       tRtV tR# )TestZmapi5  zx, yc                    VP                  V4      VP                  V4      r!WP                  V4      ,
          VP                  V^ R7      ,          p\        P                  ! W4      p\        WT4       R# )ry   rr   N)rY   r^   r   r[   zmapr/   )rc   rf   rg   rd   r  r,  s   &&&&  rm   	test_zmapTestZmap.test_zmap8  sR     zz!}bjjm1
NbffQ1f&==JJq$rp   c                   VP                  . RO. RO. RO.4      pRpRpR	p\        P                  ! W"^ R7      p\        P                  ! W"^R7      pV) V) ^,          V) ^,          R .R WU) ^,          V.W5) ^,          WS) ..p. R
OV) V) V) R.. RO.p	VP                  V4      pVP                  V	4      p	\        Wh4       \        Wy4       R# r   r>   Nr   r   r   r   )r   r   r   r   )r   r   r   r   .!	?gLXz?3Ey?;f?rP  rP  r   r   )r   rP  r   rP  rY   r[   rY  r/   
rc   rd   rf   t1t2t3z0rS  z0_expectedz1_expecteds
   &&        rm   test_zmap_axisTestZmap.test_zmap_axisE  s    JJ,,,. / ZZ1%ZZ1%bSURCE3/RQ+CE2s+- .bS2#w/-/ jj-jj-((rp   c                   VP                  . RO. RO.4      p\        P                  ! W"^^R7      pVP                  . RO4      R,          pVP                  . RO4      R,          p\        VR	,          V4       \        VR
,          V4       R# r   )r?   rN  Nr^  )r   r   r   r   )      ro  r1   r1   g3Ey?)      ro  r1   r2   g4?ry   r   rW   r   rc  rc   rd   rf   r,  ri  rj  s   &&    rm   test_zmap_ddofTestZmap.test_zmap_ddof^  ss    JJ,,. / JJq!!,jj!78*Ejj!78D$-$-rp   rN  c                   VP                  RR^\        P                  .4      pVP                  RR^^^\        P                  .4      p\        P                  ! W4VRR7      p\        P                  ! W4R,          VR7      p\        WV4       R# )	r   r   rN  r   :Nrw   NrM  NrV   rU   )rY   r   rb   r[   rY  r/   )rc   rN  rd   scorescomparer,  r  s   &&&    rm   test_zmap_nan_policy_omit"TestZmap.test_zmap_nan_policy_omitj  sn     RQ/0**b"aB78JJvTfE jj48rp   c                   VP                  VP                  RR4      R4      p\        P                   ! \        P                  ! R^^4      R4      p\        P                  VR	&   \        P                  VR
&   \        P                  VR&   VP                  VR,          \        P                  ! VR,          4      ( ,          4      pVP                  VR,          \        P                  ! VR,          4      ( ,          4      pVP                  V4      p\        P                  ! W4R^VR7      p\        P                  ! VR,          VVR7      p\        P                  ! VR,          VVR7      p	VP                  W34      p
\        Wz4       R# )r8   r   r   )r   r?   rN  rM  N      rE   rU   rx  )ry   r   rx   r  rq  rr  )r]   r   r   r5  rb   rY   rw  r[   rY  stackr/   )rc   rN  rd   ry  rz  compare_0_notnacompare_1_notnar,  r  r  r  s   &&&        rm   #test_zmap_nan_policy_omit_with_axis,TestZmap.test_zmap_nan_policy_omit_with_axisv  s   BIIdC0':**R[[Q3W= **WT]BHHWT]4K3K%LM**WT]BHHWT]4K3K%LM**W%JJv6Mzz&,#%zz&,#%88TL)$rp   Tlazy arrays don't do 'raise'.r   c                    VP                  . RO4      pVP                  RR^^^VP                  .4      p\        P                  ! \        RR7      ;_uu_ 4        \
        P                  ! W#RR7       RRR4       R#   + '       g   i     R# ; i)	rW   zinput contains nanr   r   r   Nr  rx  rV   )rY   rb   r   r   r   r[   rY  )rc   rd   ry  rz  s   &&  rm   test_zmap_nan_policy_raise#TestZmap.test_zmap_nan_policy_raise  s_    I&**b"aB78]]:-ABBJJv7; CBBBs   A<<B	5ignore:divide by zero encountered:RuntimeWarning:dask4ignore:invalid value encountered:RuntimeWarning:daskc                `   VP                  ^4      pVP                  ^4      pVP                  VP                  ) VP                  VP                  .4      p\        V\        RR7      ;_uu_ 4        \        P                  ! W#4      pRRR4       \        XV4       R#   + '       g   i     L; i)r   Precision loss occurred...r   N)
r   r  rY   r!  rb   r'   r   r[   rY  r0   )rc   rd   ry  rz  r  r   s   &&    rm   test_degenerate_inputTestZmap.test_degenerate_input  sy     1''!*jj266'266266237STT**V-C US! UTs   0BB-	c                    \         P                  ! VP                  . RO4      VP                  . RO4      4      pVP                  . RO4      p\        W#4       R# )rW   Nr  )rW                 ?rU   r  )y      ?        y       @        y      @        y      @        )r[   rY  rY   r/   )rc   rd   r   r  s   &&  rm   test_complex_gh22404TestZmap.test_complex_gh22404  s<    jjL12::>N3OPjj9:!rp   r   NrD  r  )r   r   r   r   r   )r   r   r   r   r   r   r  rZ  rk  rt  r{  r  r   r  r   r  r  r   r   r   s   @rm   rW  rW  5  s     [[
,	-
,	-	/
%
%)2
. [[VaV,	  -	  [[VaV,% -%( .MN< O< [[ WX[[ VW" X Y" [[ WX" Y"rp   rW  c                   
  a  ] tR tRt o R tR tR tR tR tR t	]
! RR	R
7      R 4       tR t]P                  P                  R4      R 4       t]P                  P                  R4      R 4       t]P                  P                  R4      R 4       t]P                  P                  R4      R 4       t]P                  P)                  R]P,                  ! . 4      ]P.                  ! R4      .4      R 4       t]R 4       tRtV tR# )
TestZscorei  c                    \         P                  ! VP                  . RO4      4      p. ROp\        W!P                  V4      4       R# )rW   Nr  )gOT\wg%ܿg%?gOT\w?)r[   zscorerY   r/   )rc   rd   rg   desireds   &&  rm   test_zscoreTestZscore.test_zscore  s3     LLL126::g./rp   c                   VP                  . RO. RO. RO.4      pRpRpR	p\        P                  ! V^ R7      p\        P                  ! V^R7      pV) V) ^,          V) ^,          R .R WU) ^,          V.W5) ^,          WS) ..p. R
OV) V) V) R.. RO.p	\        WaP                  V4      4       \        WqP                  V	4      4       R# r]  rY   r[   r  r/   rd  s
   &&        rm   test_zscore_axisTestZscore.test_zscore_axis  s    JJ,,,. / \\!!$\\!!$bSURCE3/RQ+CE2s+- .bS2#v.-/ 	JJ{34JJ{34rp   c                   VP                  . RO. RO.4      p\        P                  ! V^^R7      pVP                  . RO4      R,          pVP                  . RO4      R,          p\        VR	,          V4       \        VR
,          V4       R# rn  r  rs  s   &&    rm   test_zscore_ddofTestZscore.test_zscore_ddof  ss    JJ,,. / LL+jj!78*Ejj!78+F$-$-rp   c                    VP                  ^^\        P                  ^^.4      p\        P                  ! VRR7      p\        W1P                  VP                  VP                  4      4       R# )rW   r  r   N)rY   r   rb   r[   r  r0   r~   r  rc   rd   rf   r,  s   &&  rm   test_zscore_nan_propagate$TestZscore.test_zscore_nan_propagate  sJ    JJ1bffa+,LL{377177BFF34rp   c                    VP                  ^^VP                  ^^.4      p\        P                  ! VRR7      pVP                  RRVP                  RR.4      p\	        W44       R# )rW   r   r   gIHb=?gIHb=?NgIHb=gIHb=)rY   rb   r[   r  r/   rc   rd   rf   r,  r  s   &&   rm   test_zscore_nan_omitTestZscore.test_zscore_nan_omit  s_    JJ1bffa+,LLv.::22!vv11	! " 	$rp   c                $   VP                  VP                  R RRRR.4      p\        P                  ! V^RR7      pVP	                  VP                  VP                  .4      \        P                  ! VR,          ^R7      .4      p\        W44       R	# )
r   r   r8   r   r   r   rw  r  rM  N)rY   rb   r[   r  concatr/   r  s   &&   rm   test_zscore_nan_omit_with_ddof)TestZscore.test_zscore_nan_omit_with_ddof  sl    JJS#sC89LLv699bjj"&&2ELL2Q4OPQ$rp   Tr  r   c                    VP                  ^^VP                  ^^.4      p\        P                  ! \        RR7      ;_uu_ 4        \
        P                  ! VRR7       RRR4       R#   + '       g   i     R# ; i)rW   zThe input contains nan...r   r   r   N)rY   rb   r   r   r   r[   r  r   s   && rm   test_zscore_nan_raise TestZscore.test_zscore_nan_raise  sO    JJ1bffa+,]]:-HIILLw/ JIIIs   A((A9	c                0   VP                  R.^,          4      p\        V\        RR7      ;_uu_ 4        \        P                  ! V4      pRRR4       \        XVP                  VP                  VP                  4      4       R#   + '       g   i     LB; i)gʡE?r  r   NgʡE)	rY   r'   r   r[   r  r0   r~   r  rb   r  s   &&  rm   test_zscore_constant_input_1d(TestZscore.test_zscore_constant_input_1d  s`    JJx!|$N2NOOQA P277177BFF34 POs   BB	r  c                   VP                  . RO. RO.4      p\        V\        RR7      ;_uu_ 4        \        P                  ! V^ R7      pRRR4       \        XVP                  VP                  RRR.VP                  RRR..4      4       \        V\        RR7      ;_uu_ 4        \        P                  ! V^R7      pRRR4       \        XVP                  VP                  VP                  VP                  VP                  VP                  .4      \        P                  ! VR	,          4      .4      4       \        P                  ! VRR7      p\        WQP                  \        P                  ! VP                  VR
4      4      VP                  4      4       VP                  R4      p\        V\        RR7      ;_uu_ 4        \        P                  ! VRR7      pRRR4       \        WQP                  VP                  VP                  4      4       R#   + '       g   i     EL; i  + '       g   i     ELv; i  + '       g   i     Li; i)r   r  r   r>   Nr   r   r   r   r   r   r  r        *@rP  rr  rU   )r   rz   )rY   r'   r   r[   r  r/   rb   r0   r  r]   r  r  r~   )rc   rd   rf   rh  rS  r,  rg   s   &&     rm   test_zscore_constant_input_2d(TestZscore.test_zscore_constant_input_2d  s   JJ002 3N2NOOaa(B PBJJtT(B)+c3(?(A B 	C N2NOOaa(B PBHHbjj"&&"&&"&&"&&1Q&R&+ll1T7&;&= > 	? LL&::ell2::a3G&H!''RSGGFON2NOOQT*A P77177BFF34! POO
 POO POs#   H&H,I H)	,H=	 I	c                z   VP                  . R	OR RRVP                  .R RVP                  R ..4      pR
pRp\        V\        RR7      ;_uu_ 4        \        P
                  ! VR^ R7      pRRR4       \        XVP                  VP                  V) RVP                  .VP                  ^ RVP                  .VP                  W1P                  VP                  ..4      4       \        V\        RR7      ;_uu_ 4        \        P
                  ! VR^R7      pRRR4       \        XVP                  VP                  VP                  VP                  VP                  .V) ^ W1P                  .V) ^,          WAP                  V) ^,          ..4      4       R#   + '       g   i     EL4; i  + '       g   i     L; i)r   r  r  r  r   r   r   r?   Nr   r  r_  ra  rP  )rY   rb   r'   r   r[   r  r/   )rc   rd   rf   r  s2rh  rS  s   &&     rm   -test_zscore_constant_input_2d_nan_policy_omit8TestZscore.test_zscore_constant_input_2d_nan_policy_omit
  sk   JJ0tT2662tRVVT24 5 N2NOOaF;B PBJJ!T266(B)+C(@)+FFBFF(C(E F 	G N2NOOaF;B PBJJ(H*+Q66(:*,QFFRCE(B(D E 	F POO POs   F=F*F'	*F:	c           	        VP                  \        P                  \        P                  \        P                  \        P                  .. RO.4      p\        P                  ! VR^R7      p\        W1P                  \        P                  \        P                  \        P                  \        P                  .. RO.4      4       R# )r   r   r  N)r   r   r  r  rb  )rY   r   rb   r[   r  r/   r  s   &&  rm   test_zscore_2d_all_nan_row%TestZscore.test_zscore_2d_all_nan_row  s     JJ802 3LLvA6::'G'='? @ 	Arp   c                    VP                  RVP                  4      p\        P                  ! VRRR7      p\	        W24       R# )rE   r   Nr  rW  )r~   rb   r[   r  r0   )rc   rd   rg   r,  s   &&  rm   test_zscore_2d_all_nan!TestZscore.test_zscore_2d_all_nan'  s2     GGFBFF#LLvD9rp   rf   c                j    VP                  V4      p\        P                  ! V4      p\        W14       R # r  )rY   r[   r  r0   )rc   rf   rd   r,  s   &&& rm   test_zscore_empty_input"TestZscore.test_zscore_empty_input.  s$    JJqMLLOrp   c                ,   \         P                  P                  R 4      pVP                  ^
4      p\         P                  ! V4      p\         P
                  P                  W44      pRVP                  ^ &   \        P                  ! VR,          4      p\         P                  ! \         P                  ! V4      4      '       d   Q h\        P                  ! V4      p\        VR,          V4       \        P                  ! VRR7      p\        VR,          V4       V^,          VR&   \        P                  ! \        RR7      ;_uu_ 4        \        P                  ! V4      pRRR4       \!        VR,          \         P"                  4       \        P                  ! \        RR7      ;_uu_ 4        \        P                  ! VRR7      pRRR4       \!        VR,          \         P"                  4       R#   + '       g   i     L; i  + '       g   i     LF; i)i_ Tr  Nr>   r  r   )r   r  r  standard_normal
zeros_likerx  masked_arraymaskr[   r  anyrw  r
   r   rb  r   r   rb   )rc   rd   r  rf   r  rg   r  r   s   &&      rm   $test_zscore_masked_element_0_gh19039/TestZscore.test_zscore_masked_element_0_gh190394  sQ    ii##G,#}}QEEq'q	ll1R5!66"((3-((((ll1oB%ll14(B%!"\\.0LMM,,q/C NSWbff%\\.0LMM,,qt,C NSWbff% NM NMs   G0,H0H 	H	r   N)r   ry   rw   )r   r   r   r   r  r  r  r  r  r  r   r  r  r   r   r   r  r  r  r  r  r   r   rY  r  r%   r  r   r   r   s   @rm   r  r    s-    05.
.5
%% .MN0 O0
5 [[ VW5 X5* [[ VWF XF& [[ VWA XA [[ VW X [[S288B<)1D"EF G
 & &rp   r  c                   6   a  ] tR tRt o R t]R 4       tRtV tR# )TestGZscoreiM  c           	        \         P                  ! . RO4      p\        P                  ! VP                  V4      4      p\         P                  ! V\        P
                  ! V4      ,          4      \         P                  ! \        P                  ! V^ R7      4      ,          p\        W1P                  WAP                  R4      P                  R7      4       R# )rW   rM  r   r6   Nr  )	r   rY   r[   gzscoreloggmeangstdr/   r7   )rc   rd   rf   r,  r  s   &&   rm   test_gzscore_normal_array%TestGZscore.test_gzscore_normal_arrayO  s{    JJ|$MM"**Q-(&&U[[^+,rvvejj6K/LL::gZZ^5I5I:JKrp   c                   \         P                  ! . RO4      p. ROp\         P                  P                  WR7      p\        P
                  ! V4      pRR\         P                  RR.p\         P                  P                  WRR7      p\        VP                  4       VP                  4       4       \        VP                  VP                  4       \        V\         P                  P                  4      '       g   Q hR# )	rW   r  g/A?g(/?N)rW   rE   rU   r   r   )ry   ry   rW   ry   ry   g0jg`ȿ)r   r   rx  r  r[   r  r!  r
   
compressedr  r7  MaskedArray)rc   rf   r  mxr,  r  s   &     rm   test_gzscore_masked_array%TestGZscore.test_gzscore_masked_arrayU  s    HH%&UU-MM"#_bffn"$%%$$W$8(:(:(<=-!RUU..////rp   r   N)	r   r   r   r   r  r%   r  r   r   r   s   @rm   r  r  M  s     L 
0 
0rp   r  c            
         a  ] tR tRt o R tR tR tR tR t]	P                  P                  R. RO4      R	 4       t]	P                  P                  R
R]P                  ! ]P                  RR.4      3R]P                  ! ]P                  ]P                  R.4      3.4      R 4       t]	P                  P                  R^. RO3R.4      R 4       tR tRtV tR# )TestMedianAbsDeviationic  c                    \         P                  ! R R RRRRRRRRRRR	R	R	R
RRRRRRR\         P                  .4      V n        \         P                  ! . RO4      V n        R# )皙@r  rt   皙@r  333333@=
ףp=@r  (\
@r  r  r  皙@)\(@Q@N)r  r  r  r  rt   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  g33333<@)r   r   rb   dat_nandatr|  s   &rm   setup_class"TestMedianAbsDeviation.setup_classd  sg    xxtS#sCc!%tT4c3!$c3S$bff!N O 88 ? @rp   c                   \        \        P                  ! V P                  R R7      R4       V P                  P	                  ^^4      p\        P                  ! V^ R7      p\
        P                  ! . RO4      p\        W#4       R # )Nr>   gQ?)gףp=
?r1   ?rn  )r   r[   median_abs_deviationr  r]   r   rY   r   )rc   r  madmad_expecteds   &   rm   test_median_abs_deviation0TestMedianAbsDeviation.test_median_abs_deviationl  s_    E66txxdK!	#hhq!$((15zz"9:!#4rp   c                b    \         P                  ! V P                  R R7      p\        VR4       R# )r   r   g(\?N)r[   r  r  r   )rc   r  s   & rm   test_mad_nan_omit(TestMedianAbsDeviation.test_mad_nan_omitt  s"    ((&IC&rp   c                    \         P                  ! R RRR\         P                  .. RO.4      p\        P                  ! V^R7      p\        V\         P                  ! \         P                  R.4      4       R# )r   r   r   r   r>   N)r   r   r8   r   r   r   r   rb   r[   r  r   )rc   rf   r  s   &  rm   test_axis_and_nan(TestMedianAbsDeviation.test_axis_and_nanx  sV    HHsCc2662/1 2((3S"((BFFC=12rp   c           	         \         P                  ! ^^^^^c\         P                  \         P                  .4      p\        P
                  ! VRR7      p\        VR4       R# )rW   r   r   r   N)r   r   rb   r!  r[   r  r   )rc   r,  r  s   &  rm   test_nan_policy_omit_with_inf4TestMedianAbsDeviation.test_nan_policy_omit_with_inf~  sC    HHaAq"bffbff56((v>S#rp   r?   Nc           	         \         P                  ! R4      p\        P                  ! W!R7      p\	        V\         P
                  ! VP                  VR7      \         P                  R7      4       R# )r   r>   
fill_valueN)r   ry   r   )r   rY  r[   r  r   	full_liker^  rb   )rc   r?   rf   r  s   &&  rm   test_size_zero_with_axis/TestMedianAbsDeviation.test_size_zero_with_axis  sD    HHY((6S",,quu$u'7BFFKLrp   znan_policy, expectedr   r2   r  c           	     z   \         P                  ! \         P                  \         P                  \         P                  \         P                  \         P                  \         P                  .^^^^\         P                  \         P                  .. RO.4      p\        P                  ! W1^R7      p\        WB4       R# )rW   r  N)rw   rz   rJ   rI   rI   rO   r  )rc   r   r  rf   r  s   &&&  rm   test_nan_policy_with_axis0TestMedianAbsDeviation.test_nan_policy_with_axis  su     HHrvvrvvrvvrvvrvvrvvF!Q2662662)+ , ((JS#rp   zaxis, expectedc                    \         P                  ! ^^^^	\         P                  .. RO. RO.4      p\        P                  ! V\         P
                  RVR7      p\        WBRRR7       R# )rW   r   )centerr   r?   rD  r  N)ry   rW   rW   rW   rQ   )r  r  r  r  )r   r   rb   r[   r  r^   r
   )rc   r?   r  rf   r  s   &&&  rm   test_center_mean_with_nan0TestMedianAbsDeviation.test_center_mean_with_nan  sY     HHq!Q266*&-/ 0 ((277v.24E>rp   c                    \         P                  ! \        R R7      ;_uu_ 4        \        P                  ! . RO^cR7       RRR4       R#   + '       g   i     R# ; i)callabler   r
  N)rW   rE   r   rw   )r   r   r&  r[   r  r|  s   &rm   test_center_not_callable/TestMedianAbsDeviation.test_center_not_callable  s2    ]]9J77&&|B? 8777s   A

A	)r  r  )ry   rW   rE   N)rt   r   r  )NrA   )r   r   r   r   r  r  r  r  r  r   r   r  r  r   r   rb   r  r  r  r   r   r   s   @rm   r  r  c  s     @5'3
 [[V_5M 6M
 [[3%rxxc0B'CD*BHHbffbffc5J,KLNO$O$ [[- "23[AC?C?@ @rp   r  c                r    \        \        V 4      VR4       V  F  p\        VP                  VJ 4       K  	  R# )z
Checks that all of the warnings from a list returned by
`warnings.catch_all(record=True)` are of the required type and that the list
contains expected number of warnings.
znumber of warningsN)r   r   r   category)	warn_listexpected_typeexpected_lenwarn_s   &&& rm   _check_warningsr    s0     Y/CD-/0 rp   c                      a  ] tR tRt o R tR t]P                  P                  R. ]	P                  ! ^ 4      .4      R 4       tR tR tR tR	 tR
 tR tR tR tR tRtV tR# )TestIQRi  c                    \         P                  ! ^4      R,          p\         P                  P                  V4       \	        \
        P                  ! V4      R4       R# )rF   r1   r  N)r   r   r  r  r   r[   iqrr  s   & rm   rX  TestIQR.test_basic  s8    IIaL3
		!UYYq\4(rp   c           	        \         P                  ! R4      p\        P                  ! V4       \        P                  ! VR4       \        P                  ! V^4       \        P                  ! VR4       \        P                  ! VRR4       \        P                  ! VRRR4       \        P                  ! VRRRR4       \        P                  ! VRRRRR4       \        P                  ! VRRRRR	R
4       R# )rw   Nr   r2   r  r  r   linearr   r  Tr  rV  )rO   Z   )r  r  )r  r2  )r  r  gٿ)r   r  r[   r  )rc   rk  s   & rm   test_apiTestIQR.test_api  s    GGFO		!		!T		!Q		!V		!T8$		!T8S)		!T8S+6		!T8XwA		!T8T67DArp   rf   c                    \         P                  ! \        \        R 7      ;_uu_ 4        \	        \
        P                  ! V4      \        P                  4       RRR4       R#   + '       g   i     R# ; ir  )	r   rb  r   r   r   r[   r  r   rb   r  s   &&rm   r  TestIQR.test_empty  s;    \\,4IJJ1rvv. KJJJs   /A""A3	c                   \         P                  ! R4      p\        \        P                  ! V4      R4       \        \        P                  ! V^ R7      \         P                  ! ^4      4       \        \        P                  ! V^R7      \         P                  ! ^4      4       \        \        P                  ! VRR7      R4       \        \        P                  ! VRR7      R4       \        \        P                  ! VRR7      R4       \        \        P                  ! VRR7      R4       \        \        P                  ! VRR7      R4       \         P                  ! R4      \         P                  ! ^4      ,          p\        \        P                  ! V^ R7      \         P                  ! R4      4       \        \        P                  ! V^R7      \         P                  ! R4      4       \        \        P                  ! V^R7      \         P                  ! RR	4      4       \        \        P                  ! VRR7      \         P                  ! ^4      4       \        \        P                  ! VRR7      \         P                  ! ^R
4      4       \        \        P                  ! VRR7      \         P                  ! ^R
4      4       R# )rJ   r   r>   r   interpolationmidpointnearestr  r  rt   r   N)rJ   r   r   rw   rz   )rw   rz   )r   rz   r  rV  ry   rE   rW   rE   )	r   r  r   r[   r  r   rY  r   r~   r  s   &  rm   test_constantTestIQR.test_constant  s   GGFOUYYq\3'599QQ/!=599QQ/!=UYYq93?UYYq
;SAUYYq	:C@UYYq8#>UYYq93? GGI1-599QQ/&1AB599QQ/&1AB599QQ/1EF599QV4bhhqkB599QV4bgganE599QV4bgganErp   c                   \         P                  ! ^4      R,           p\        \        P                  ! V^ ,          4      R4       \        \        P                  ! V4      R4       \        \        P                  ! VRR7      R.4       R# )rW   r   r   Tr  N)r   r   r   r[   r  r   r  s   & rm   test_scalarlikeTestIQR.test_scalarlike  sS    IIaL3UYYqt_c*UYYq\3'599Q6>rp   c                   \         P                  ! ^4      P                  R4      p\        \        P
                  ! V4      R4       \        \        P
                  ! V^ R7      \         P                  ! ^R4      4       \        \        P
                  ! V^R7      \         P                  ! ^R4      4       \        \        P
                  ! VRR7      R4       \        \        P
                  ! VRR7      R4       R# )	r  r   r>   r8   r   Nr  rV  r  )r   r   r]   r   r[   r  r   r~   r  s   & rm   test_2DTestIQR.test_2D  s    IIbM!!&)UYYq\3'599QQ/B@599QQ/B@599QV4c:599QV4c:rp   c                ^   \         P                  P                  RR7      p\         P                  ! V.^
,          4      p\        P
                  ! V4      p\        \        P
                  ! VRR7      V4       \         P                  ! VR^ 4      p\        \        P
                  ! VRR7      V4       VP                  ^ ^4      p\        \        P
                  ! VRR7      V4       VP                  ^ ^4      p\        \        P
                  ! VR	R7      \        P
                  ! VRR7      4       \        \        P
                  ! VR
R7      \        P
                  ! V^ R7      4       \         P                  ! R4      p\         P                  P                  V4       VP                  R4      p\        \        P
                  ! VR	R7      ^ ,          \        P
                  ! VR,          P                  4       4      4       \        \        P
                  ! VRR7      ^,          \        P
                  ! VR,          P                  4       4      4       \        \        P
                  ! VRR7      ^,          \        P
                  ! VR,          P                  4       4      4       \        \        P
                  ! VRR7      ^,          \        P
                  ! VR,          P                  4       4      4       \        \        P
                  ! VRR7      R,          \        P
                  ! VR,          P                  4       4      4       \        \        P
                  ! VRR7      R,          \        P
                  ! VR,          P                  4       4      4       \        \        P
                  ! VRR7      R,          \        P
                  ! VR,          P                  4       4      4       \        \        \        P
                  V^R7       \        \        \        P
                  VRR7       R# )G   r  r>   N)r7  r  rV  rU   r  r,  r  r  i  r   rw   rJ   rP   )r   r   r   ry   ry   rW   r   )r   r   rW   r   )r   rW   rA  )r   r   rE   r   )r   rW   rE   )rE   r   r   r   r   rE   )rE   rW   r   r   )rW   rZ  )rE   r   r   rW   )rW   r   rE   rE   )rE   r   rE   r   r  )r   r  r  dstackr[   r  r   moveaxisswapaxesr   r  r]   r  r   r$   r   )rc   orf   qrk  s   &    rm   r  TestIQR.test_axis  s   II(+IIqcBhIIaLUYYqv.2KK2q!UYYqv.2JJq!UYYqv.2JJq!UYYqy1YYqt,	.UYYqt,YYqq)	+ IIn% 			!IIm$UYYqy1!4YYq{0023	5UYYqy1!4YYq{0023	5UYYqz215YYq{0023	5UYYqy1!4YYqz//12	4UYYqv.t4YYq{0023	5UYYqw/5YYq}2245	7UYYqv.t4YYq|1134	6 	iAA6j%))QV<rp   c                $   \         P                  ! ^4      p\        \        P                  ! V4      ^4       \        \        P                  ! VRR7      R4       \        \        P                  ! VRR7      R4       \        \        P                  ! VRR7      R4       \        \        \        P                  VRR7       \        \        \        P                  V\         P                  ^3R7       \        \        \        P                  VR	R7       R# )
rw   r  rt   g?N)r  g     U@)g      )@r2  )rO   r  )ry   e   )ry   r  <   )
r   r   r   r[   r  r   r   r   rb   r&  r  s   & rm   test_rngTestIQR.test_rng  s    IIaLUYYq\1%UYYqj137UYYqj137EIIaX6<j%))QH=j%))QRVVRLAiA;?rp   c                   \         P                  ! ^4      p\         P                  ! ^4      p\        \        P                  ! V4      ^4       \        \        P                  ! V4      R4       \        \        P                  ! VRR7      ^4       \        \        P                  ! VRR7      R4       \        \        P                  ! VRR7      ^4       \        \        P                  ! VRRR7      ^4       \        \        P                  ! VRR7      ^4       \        \        P                  ! VRR7      ^4       \        \        P                  ! VRRR7      ^4       \        \        P                  ! VRR7      ^4       \        \        P                  ! VRR7      ^4       \        \        P                  ! VRR7      ^4       \        \        P                  ! VRR7      ^4       \        \        P                  ! VRRR7      R	4       \        \        P                  ! VRR7      ^4       R F  p\        P                  ! W#R7       K  	  \        \        \        P                  VR
R7       R# )rw   r2   r   r'  r  )r  r(  r  r*  r)  rt   r   N)r  P   )inverted_cdfaveraged_inverted_cdfclosest_observationinterpolated_inverted_cdfhazenweibullmedian_unbiasednormal_unbiased)r   r   r   r[   r  r   r   )rc   rf   rg   r  s   &   rm   test_interpolationTestIQR.test_interpolation  s   IIaLIIaLUYYq\1%UYYq\3'UYYq91=UYYq93?UYYq91=UYYqhhGKUYYq91=UYYq8!<UYYqhgFJUYYq8!<UYYq	:A>UYYq	:A>UYYq
;Q?UYYqhjI3OUYYq
;Q?*F IIa.	* 	j%))QhGrp   c                   \         P                  ! R4      p\        \        P                  ! VRRR7      P
                  R4       \        \        P                  ! V^RR7      P
                  R4       \        \        P                  ! VR	RR7      P
                  R
4       \        \        P                  ! VRRR7      P
                  R4       \        \        P                  ! VRRR7      P
                  R4       \        \        P                  ! VRRR7      P
                  R4       \        \        P                  ! VRRR7      P
                  R4       \        \        P                  ! VRRR7      P
                  R4       \        \        P                  ! V^RR7      P
                  R4       \        \        P                  ! VR	RR7      P
                  R4       \        \        P                  ! VRRR7      P
                  R4       \        \        P                  ! VRRR7      P
                  R4       \        \        P                  ! VRRR7      P
                  R4       \        \        P                  ! VRRR7      P
                  R4       R# )r   NFr  r  Tr8  r   )r   rw   rP   rV  )rJ   rP   )ry   r   )rw   rJ   r  r  ry   rW   rE   r   r9  ru   rQ  )r   rw   rW   rP   )rW   rW   rJ   rP   )rW   rw   rJ   rW   )r   rW   rJ   rP   )rW   rW   rJ   rW   )r   r  r   r[   r  r  r  s   & rm   r  TestIQR.test_keepdims?  s   GGM"UYYqte<BBBGUYYqq59??LUYYqv>DDgNUYYqv>DDfMUYYqte<BBJOUYYq,?EErJUYYqy5AGGNUYYqtd;AA<PUYYqq48>>NUYYqv=CC]SUYYqv=CC\RUYYqtd;AA=QUYYq,>DDlSUYYqy4@FFUrp   c           
        \         P                  ! R 4      P                  R4      p\        \        P
                  ! VRR7      ^4       \        \        P
                  ! VRR7      ^4       \        \        P
                  ! VRR7      ^4       \         P                  VR&   \        P                  ! RR7      ;_uu_ 4        \        P                  ! R4       \        \        P
                  ! VRR7      \         P                  4       \        \        P
                  ! V^ RR7      ^^\         P                  ^^.4       \        \        P
                  ! V^RR7      ^\         P                  ^.4       R	R	R	4       \        P                  ! RR7      ;_uu_ 4        \        P                  ! R4       \        \        P
                  ! VRR7      R
4       \        \        P
                  ! V^ RR7      \         P                  ! ^^4      4       \        \        P
                  ! V^RR7      . RO4       R	R	R	4       \        \        \        P
                  VRR7       \        \        \        P
                  V^ RR7       \        \        \        P
                  V^RR7       \        \        \        P
                  VRR7       R	#   + '       g   i     ELV; i  + '       g   i     L; i)      .@r  r   r   r   Tr   alwaysr  N      @barfoodr  r-  )rE   rt   rE   )r   r   r]   r   r[   r  rb   warningscatch_warningssimplefilterr~   r   r   r  s   & rm   test_nanpolicyTestIQR.test_nanpolicyR  s   IIdO##F+ 	UYYq[91=UYYqV4a8UYYqW5q9 &&$$$D11!!(+1=!11EQ1-/11ERVVQ) 2 $$D11!!(+18#>11@"''!Q-P11@+N	 2 	j%))Q7Cj%))QQ7Kj%))QQ7K 	j%))Q9E) 211 21s   >B1J<BK<K	K 	c                   \         P                  ! R 4      P                  R4      p\        \        P
                  ! VRR7      ^4       \        \        P
                  ! VRR7      R4       \        \        P
                  ! VRR7      R4       \         P                  VR&   \        P                  ! RR7      ;_uu_ 4        \        P                  ! R	4       \        \        P
                  ! VRR
R7      \         P                  4       \        \        P
                  ! VRR
R7      \         P                  4       \        \        P
                  ! VRR
R7      \         P                  4       \        \        P
                  ! V^RR
R7      ^\         P                  ^.4       \        \        P
                  ! V^RR
R7      \         P                  ! ^\         P                  ^.4      R,          4       \        \        P
                  ! V^RR
R7      ^\         P                  ^.4       RRR4       \        \        P
                  ! VRRR7      R4       \        \        P
                  ! VRRR7      R4       \        \        P
                  ! VRRR7      R4       \        \        \        P
                  VRR7       R#   + '       g   i     L; i)rW  r   r$  r  gF7k?r   r  TrX  rY  r  )r$  r   )r?   r$  r   Nr   rZ  g      @r   r  g=V^w@r-  g	I1=@)r   r   r]   r   r[   r  r   rb   r\  r]  r^  r   r   r   r  s   & rm   
test_scaleTestIQR.test_scaler  s   IIdO##F+ 	UYYq,a0EIIax8-HUYYq,c2 &&$$$D11!!(+1CKH"&&Q1HMrvvV1CKH"&&Q11C.9;=>NL		!!85@!B "!RVVQ 89 DF 11CKPRVVQ) 2" 	UYYq?EEIIaxFK+	-UYYq?F 	j%))Qh?/ 21s   >E$J66K	r   N)r   r   r   r   rX  r"  r   r   r  r   r   r  r.  r1  r4  r  rE  rQ  r  r_  rc  r   r   r   s   @rm   r  r    s~     )

B [[S2ryy|"45/ 6/F,?;'=R	@ HDV&F@!@ !@rp   r  c                     a  ] tR tRt o Rt. ROtRt]P                  P                  R4       ]P                  P                  ^*4      t]P                  P                  R^
R.4      ]P                  P                  R]! RR4      4      ]P                  P!                  R4      R	 4       4       4       t]P                  P                  R^
R.4      ]P                  P                  R
R4      ]P                  P!                  R4      R 4       4       4       tR tR t]P                  P                  R. RO4      ]P                  P                  RRR .4      R 4       4       tR tR tR tR t]P                  P                  R. RO4      ]P                  P                  R. R!O4      ]P                  P                  RR^ .4      ]P                  P!                  R4      R 4       4       4       4       tRtV tR# )"TestMomentsi  aC  
Comparison numbers are found using R v.1.5.1
note that length(testcase) = 4
testmathworks comes from documentation for the
Statistics Toolbox for Matlab and can be found at both
https://www.mathworks.com/help/stats/kurtosis.html
https://www.mathworks.com/help/stats/skewness.html
Note that both test cases came from here.
r     r  zm, cNz?ignore:divide by zero encountered in divide:RuntimeWarning:daskc                r   \         P                  P                  R 4      pVP                  VP                  VR7      4      p\        P
                  ! WbVR7      pVf   VP                  V^ R7      MTpVP                  Wc,
          V,          ^ R7      VP                  ^ ,          ,          p\        WxRR7       R# )l   rHZ r  r  Nr>   缉ؗҜ<rE  )
r   r  r  rY   r[   momentr^   r^  r  r/   )	rc   r  r  rj  rd   r  rf   r   r  s	   &&&&&    rm    test_moment_center_scalar_moment,TestMoments.test_moment_center_scalar_moment  s     ii##$78JJszztz,-ll1*"#)BGGAAGffaeaZaf(3u-rp   rj  c                r   \         P                  P                  R 4      pVP                  VP                  VR7      4      p. ROp\        P
                  ! WVVR7      pTP                  V Uu. uF.  p\        P
                  ! WXVR7      VP                  R3,          NK0  	  up4      p	\        Wy4       R# u upi )l   %~.}~= r  r  .NrT  )	r   r  r  rY   r[   rj  r  newaxisr0   )
rc   r  rj  rd   r  rf   r  r   r  r  s
   &&&&      rm   test_moment_center_array_moment+TestMoments.test_moment_center_array_moment  s     ii##$78JJszztz,-ll1*iiPQRPQ1a15bjj#oFFPQRS! Ss   ,4B4c                b  a SP                  V P                  4      p\        P                  ! SP                  V P                  4      4      p\        VSP                  R 4      4       \        P                  ! V^ 4      p\        VSP                  R4      4       \        P                  ! V^4      p\        VSP                  R 4      4       \        P                  ! V^4      p\        VSP                  R4      4       \        P                  ! V^4      p\        VSP                  R 4      4       \        P                  ! V^4      p\        VSP                  R4      4       \        P                  ! V. RO4      p\        VSP                  . RO4      4       \        P                  ! VR 4      p\        VSP                  R4      4       Rp\        P                  ! \        VR7      ;_uu_ 4        \        P                  ! VR4       RRR4       \        P                  ! V. RO4      p\        VSP                  . RO4      4       V3R lp\        S4      '       d7   \        P                  ! \        R	R7      ;_uu_ 4        V! 4        RRR4       R# \        P                  P                  4       ;_uu_ 4       pVP                  \         R
4       VP                  \         R4       V! 4        RRR4       R#   + '       g   i     L; i  + '       g   i     R# ; i  + '       g   i     R# ; i)r   r         ?     @z)All elements of `order` must be integral.r   333333?Nc                    < \         P                  ! SP                  . 4      4      p \        V SP                  SP                  4      4       \         P                  ! SP                  . SP
                  R 7      4      p \        V SP                  SP                  SP
                  R 7      4       \         P                  ! SP                  R4      ^ R7      p \        V SP                  R4      4       \         P                  ! SP                  . .4      ^R7      p \        V SP                  SP                  .4      4       \         P                  ! SP                  . .4      ^ ^.^ R7      p \        V SP                  R4      4       R# )r6   r>   orderr?   Nr  r  )rE   ry   )r[   rj  rY   r0   rb   r   rY  rB  )rg   rd   s    rm   
test_cases+TestMoments.test_moment.<locals>.test_cases  s   RZZ^,AArzz"&&12RZZ"**Z=>AArzz"&&

zCDRXXf-A6AArxx~.RZZ-A6AArzz266(34RZZ-aV!DAArxx/0rp   zSee documentation for...zMean of empty slice.zinvalid valuer  )ry   rr  ry   rs  )r   rE   r   r   )rY   rO  r[   rj  rG  r/   r   r   r   r)   rb  r   r   r"  r   r   r   )rc   rd   rO  rg   r  rx  r   s   &f     rm   test_momentTestMoments.test_moment  s   ::dmm,LLD$8$89:2::c?+LL1%2::c?+LL1%2::c?+LL1%2::d+,LL1%2::c?+LL1%2::f-. LL<02::&:;< LL3'2::c?+=]]:W55LL3' 6LL#342::&:;<
	1 B<<08RSS TS --//3

>+AB

>?; 0/- 65& TSS 0//s$   /K6 L	84L6L		L	L.	c                ~   \         P                  ! R 4      p\         P                  V^	&   \        \        P
                  ! V^4      \         P                  4       \        \        P
                  ! VRR7      R4       \        \        \        P
                  VRR7       \        \        \        P
                  VRR7       R# )r   r   r   r   r   r   N)	r   r   rb   r   r[   rj  r   r   r   r  s   & rm   r  TestMoments.test_nan_policy  sn    IIcNvv!U\\!Q'0ELLv>Dj%,,gFj%,,hGrp   r7   zexpect, orderc           	        VR 8X  d'   \        V4      '       d   \        P                  ! 4        \        WA4      pVP	                  \
        P                  P                  ^4      VR7      p\        P                  ! WSR7      p\        WdP	                  W!R7      4       \        P                  ! VP                  VR4      ^ VR7      p\        WdP                  RW!R7      4       \        P                  ! VP                  VR4      ^VR7      p\        WdP                  RW!R7      4       \        P                  ! VP                  VR4      RVR7      p\        WdP                  R	W!R7      4       R# )

complex128r6   rw  )r?   rw  N)rz   rw   )rw   r  )rW   rE   r   rw   r   )r*   r   skiprj  rY   r   r  r  r[   rj  r0   broadcast_tor~   )rc   r7   expectrw  rd   rf   rg   s   &&&&&  rm   test_constant_moments!TestMoments.test_constant_moments  s    ,8B<<KKM"JJryy~~a(J6LL(::f::;LLF3!5I7747=>LLO<1$&77<7EFLLO<4$&772v7;<rp   c                T   VP                  VP                  R 4      R4      p\        P                  ! V4      R,          P	                  VP
                  4      p\        P                  ! VP                  V4      ^^R7      p\        W1P                  RVP
                  .4      RR7       R# )r   r>   rr  rD  rE  Nr  r  )
r]   r   r_   r`   ra   rb   r[   rj  rY   r/   )rc   rd   rK  mms   &&  rm   test_moment_propagate_nan%TestMoments.test_moment_propagate_nan  sq     JJryy}g.FF1IdO'\\"**Q-3JJbff~6UCrp   c                    \         P                  ! \        R R7      ;_uu_ 4        \        P                  ! VP                  . RO4      . R7       RRR4       R#   + '       g   i     R# ; i)z1`order` must be a scalar or a non-empty 1D array.r   r  Nr  )r   r   r   r[   rj  rY   rc   rd   s   &&rm   test_moment_empty_order#TestMoments.test_moment_empty_order  sM    ]]: .E F FLLL1<F F F Fs   *AA*	c                    VP                  ^
4      p\        P                  ! V^R7      p\        P                  ! V^R7      p\        W44       R# )rO   )rj  r  N)r   r[   rj  r0   )rc   rd   rf   r   r  s   &&   rm   test_rename_moment_order$TestMoments.test_rename_moment_order!  s9     IIbMll1Q'll1A&!rp   c                   V P                   \        P                  ! V P                   4      ,
          p\        \        P                  ! V^*4      P                  4       \
        P                  ! V P                   ^*4      4       R# r  )testcase_moment_accuracyr   r^   r
   r   r[   rj  )rc   
tc_no_means   & rm   test_moment_accuracy TestMoments.test_moment_accuracy)  sY     33 = =>?
R0557T%B%BBG	Irp   rw  r?   r
  c           	        \         P                  P                  R 4      pVP                  RR7      p\        P                  ! VP                  V4      W#VR7      pVP                  \        WbW4R7      4      p\        Wx4       R# )l   hU~r  )r?   r
  )r^   N)rw   rz   rJ   )r   r  r  r[   rj  rY   r   r/   )	rc   rd   rw  r?   r
  r  rf   r   r  s	   &&&&&    rm   test_moment_array_api!TestMoments.test_moment_array_api1  s_     ii##N3JJIJ&ll2::a=%6Jjj4=>!rp   r   rD  )rO   rE   rT  )Nry   rW   )r   r   r  rV  r  rT  )r   r   r   r   r5  rO  rG  r   r  r  r  r  r   r   r  r   r   rk  ro  rz  r  r  r  r  r  r  r  r   r   r   s   @rm   rf  rf    s      HOIINN4!yy~~b1[[Vb']3[[VW\<%HI[[I. J 4
. [[Vb']3[[S,/[[I" 0 4
"3jH [[W&JK[[_vv.>?= @ L=&D="I [[Wl3[[VZ0[[Xay1[[I" 2 1 4"rp   rf  c                   :   a  ] tR tRt o Rt. ROt. ROtR tRtV t	R# )SkewKurtosisTesti?  r   c                >   VP                  . 4      p\        V4      '       dD   \        P                  ! \        \
        R 7      ;_uu_ 4        V P                  V4      pRRR4       Ml\        P                  P                  4       ;_uu_ 4       pVP                  \        R4       VP                  \        R4       V P                  V4      pRRR4       \        XVP                  VP                  4      4       R#   + '       g   i     L7; i  + '       g   i     LJ; i)r   NMean of empty slicezinvalid value encountered)rY   r)   r   rb  r   r   stat_funr   r"  r   r   r   r0   rb   )rc   rd   rf   r   r   s   &&   rm   test_empty_1dSkewKurtosisTest.test_empty_1dD  s    JJrNB<<08MNNmmA& ON --//3

>+@A

>+FGmmA&	 0
 	RZZ/0 ON 0/s   C9>D9D		D	r   NrD  )gp=
ף?g?߾?gD9?gQI?g}?5^I)
r   r   r   r   rG  rO  testmathworksr  r   r   r   s   @rm   r  r  ?  s     OH<M1 1rp   r  c                   (  a  ] tR tRt o R t]P                  P                  R4      R 4       tR t	R t
R tR t]! R	R
7      R 4       t]P                  P                  R. RO4      ]P                  P                  RRR	.4      R 4       4       tRtV tR# )TestSkewiR  c                .    \         P                  ! V4      # r  )r[   skewr  s   &&rm   r  TestSkew.stat_funT  s    zz!}rp   zEignore:invalid value encountered in scalar divide:RuntimeWarning:daskc                r   \         P                  ! VP                  V P                  4      4      p\	        W!P                  VP
                  4      4       \         P                  ! VP                  V P                  4      4      p\	        W!P                  R4      RR7       \         P                  ! VP                  V P                  4      ^ R7      p\	        W!P                  R4      RR7       \         P                  ! VP                  V P                  4      4      p\	        W!P                  R4      RR7       R# )g7l*?绽|=rE  biasr   Ng7l*ҿg2۠ۿ)r[   r  rY   rG  r/   rb   r  rO  )rc   rd   rg   s   && rm   test_skewnessTestSkew.test_skewnessW  s    
 JJrzz$"6"678::bff-. JJrzz$"4"456::&78uEJJrzz$"4"45A>::&89FJJrzz$--01::c?7rp   c                   \         P                  ! R 4      p\         P                  V^	&   \         P                  ! RR7      ;_uu_ 4        \	        \
        P                  ! V4      \         P                  4       RRR4       \	        \
        P                  ! VRR7      R4       \        \        \
        P                  VRR7       \        \        \
        P                  VRR7       R#   + '       g   i     Lv; i)	r   r}  r~  Nr   r   r   r   r   )	r   r   rb   r  r   r[   r  r   r   r  s   & rm   r  TestSkew.test_nan_policyg  s    IIcNvv![[**A/ +UZZf5r:j%**aGDj%**aHE	 +*s   	/C&&C6	c                X    \        \        P                  ! \        ^
4      4      R4       R# )rO   r   N)r   r[   r  r   r|  s   &rm   test_skewness_scalarTestSkew.test_skewness_scalarq  s    UZZr
+S1rp   c                   VP                  R 4      pVP                  VR4      p\        P                  ! V4      R,          P	                  VP
                  4      p\        P                  ! RR7      ;_uu_ 4        \        P                  ! VP                  V4      ^R7      pRRR4       \        XVP                  ^ VP
                  .4      4       R#   + '       g   i     L9; i)r   r}  r~  r>   Nr  r  )r   r]   r_   r`   ra   rb   r   r  r[   r  rY   r0   )rc   rd   rK  r  s   &&  rm   test_skew_propagate_nan TestSkew.test_skew_propagate_nanu  s     IIbMJJq'"FF1IdO'[[**

2::a=q1A +2::q"&&k23 +*s   9(CC"	c           	        VP                  VP                  R	.4      ^
4      p\        V\        RR7      ;_uu_ 4        \	        \
        P                  ! V4      VP                  VP                  4      4       \	        \
        P                  ! VR
,          4      VP                  VP                  4      4       \	        \
        P                  ! VR
,          4      VP                  VP                  4      4       \	        \
        P                  ! VRR7      VP                  VP                  4      4       VP                  R.^,          4      p\	        \
        P                  ! V4      VP                  VP                  4      4       RVP                  R^4      R,          ,           p\	        \
        P                  ! V4      VP                  VP                  4      4       RRR4       R#   + '       g   i     R# ; i)9?Precision loss occurredr   Fr  g,@r   ri  N9ѿg      C      )	repeatrY   r'   r   r0   r[   r  rb   r   rc   rd   rK  s   && rm   test_skew_constant_value!TestSkew.test_skew_constant_value  s4   IIbjj+/4N2KLLEJJqM2::bff+=>EJJqx0"**RVV2DEEJJqx0"**RVV2DEEJJqu5rzz"&&7IJ 

D6!8$AEJJqM2::bff+=>RYYsA&u,,AEJJqM2::bff+=> MLLLs   F G''G8	Tr   c                >   \         P                  ! \        R R7      ;_uu_ 4        \        P                  P                  R4      pVP	                  RR7      pRVR&   \        P                  ! VP                  V4      4       RRR4       R#   + '       g   i     R# ; i)r  r   l   :"z` r  )\(?N)r  rO   r   ry   )	r   rb  r   r   r  r  r[   r  rY   )rc   rd   r  rK  s   &&  rm   test_precision_loss_gh15554$TestSkew.test_precision_loss_gh15554  sg    
 \\.0IJJ))''4C

	
*AAdGJJrzz!}%	 KJJJs   ABB	r?   Nr  Fc                   a \         P                  P                  R 4      pSP                  VP                  R4      4      pV3R lp\        P
                  ! WRVR7      pV! WRVR7      p\        Wx4       R# )   f#"c                 l  < Vf   SP                  V R4      p ^ pSP                  WRR7      pSP                  W,
          ^,          VR7      pSP                  WR7      pWE^,          ,          pV'       g?   V P                  V,          pWgR,
          V,          R,          VR,
          ,          ,          pV# )NTr  r>   r   r1   r   r  )r]   r^   r   r  )	rK  r?   r  r^   mu3r   r   r  rd   s	   &&&     rm   skewness-TestSkew.test_vectorization.<locals>.skewness  s    |JJq%(771$77D''18a-d'3C&&&&Cq.CGGDMSA#-S99Jrp   )r?   r  Nr  )r   r  r  rY   r[   r  r/   )	rc   rd   r?   r  r  rf   r  r   r  s	   &f&&     rm   test_vectorizationTestSkew.test_vectorization  s[    
 ii##M2JJszz),-	 jjD1q$/!rp   r   rU   ry   rE   N)r   r   r   r   r  r   r   r   r  r  r  r  r  r   r  r  r  r   r   r   s   @rm   r  r  R  s      [[O88F24?  && '& [[V%56[[VeT]3" 4 7"rp   r  c                   L  a  ] tR tRt o R t]P                  P                  R4      R 4       tR t	R t
R tR t]P                  P                  R	. RO4      ]P                  P                  RRR.4      ]P                  P                  RRR.4      R 4       4       4       tRtV tR
# )TestKurtosisi  c                .    \         P                  ! V4      # r  )r[   kurtosisr  s   &&rm   r  TestKurtosis.stat_fun  s    ~~a  rp   z1ignore:invalid value encountered in scalar dividec                2   \         P                  ! VP                  V P                  4      4      pVP	                  V4      '       g   Q h\         P                  ! VP                  V P
                  4      ^ ^ ^R7      p\        W!P                  R4      4       \         P                  ! VP                  V P
                  4      ^ ^ R7      p\        W!P                  R4      4       \         P                  ! VP                  V P                  4      ^ ^ 4      p\        W!P                  R4      4       VP                  R4      pVP                  V^8H  VP                  V4      p\        \         P                  ! V4      VP                  VP                  4      4       R# )ry   fisherr  gO߻S@gx|N@g=
ףp=?r   N)r[   r  rY   rG  rw  r  r/   rO  r   rP  rb   r0   )rc   rd   rg   rf   s   &&  rm   test_kurtosisTestKurtosis.test_kurtosis  s    NN2::d&:&:;<xx{{{ NN2::d&8&891QQO::o67 NN2::d&8&89!!L::&789NN2::dmm4a;::d+,IIcNHHQ!VRVVQ'q)2::bff+=>rp   c                    \         P                  ! R 4      p\         P                  V^	&   \        \        P
                  ! VRR7      R4       \        \        \        P
                  VRR7       \        \        \        P
                  VRR7       R# )r   r   r   r   r   NGz)r   r   rb   r   r[   r  r   r   r  s   & rm   test_kurtosis_nan_policy%TestKurtosis.test_kurtosis_nan_policy  sU    IIcNvv!ENN1@)Lj%..!Hj%..!Irp   c                x    \        \        \        P                  ! . RO4      4      \        P
                  4       R# r  )r   typer[   r  r   r   r|  s   &rm   test_kurtosis_array_scalar'TestKurtosis.test_kurtosis_array_scalar  s    T%..34bjjArp   c                4   \         P                  ! ^4      P                  ^R4      P                  \        4      p\         P
                  VR&   \        P                  ! V^RR7      p\         P                  P                  VR\         P
                  .RR7       R# )	rF   r  r  rD  rE  NrU   r  g(\)
r   r   r]   r  r  rb   r[   r  r"  r
   )rc   rK  r  s   &  rm   test_kurtosis_propagate_nan(TestKurtosis.test_kurtosis_propagate_nan  si     IIaL  B'..u5&&$NN11=


""1ubffoE"Brp   c           
     b   VP                  R.^
,          4      p\        V\        RR7      ;_uu_ 4        VP                  \        P
                  ! VRR7      4      '       g   Q hVP                  \        P
                  ! V\        R4      ,          RR7      4      '       g   Q hVP                  \        P
                  ! V\        R4      ,          RR7      4      '       g   Q hVP                  \        P
                  ! VRRR7      4      '       g   Q h RRR4       R#   + '       g   i     R# ; i)	r  r  r   F)r  r  Nr  l           )rY   r'   r   rw  r[   r  r  r  s   && rm   test_kurtosis_constant_value)TestKurtosis.test_kurtosis_constant_value  s    JJ}R'(N2KLL88ENN1U;<<<<88ENN1uU|+;EJKKKK88ENN1uU|+;EJKKKK88ENN1UGHHHH	 MLLLs   CDDD.	r?   Nr  FTr  c                   a \         P                  P                  R 4      pSP                  VP                  R4      4      pV3R lp\        P
                  ! WbW4R7      pV! WbW4R7      p	\        W4       R# )r  c                   < Vf   S	P                  V R4      p ^ pS	P                  WRR7      pS	P                  W,
          ^,          VR7      pS	P                  W^ R7      pV'       d   WV^,          ,          ^,
          pMpV P                  V,          pV^,
          V^,
          V^,
          ,          ,          V^,           V,          V^,          ,          ^V^,
          ,          ,
          ,          pV'       d   V# V^,           # )NTr  r>   r?   rs   r  )r]   r^   r}   r  )
rK  r?   r  r  r^   mu4mu2r   r  rd   s
   &&&&     rm   r  1TestKurtosis.test_vectorization.<locals>.kurtosis  s    |JJq%(771$77D''18a-d'3C&&!&4CFlQ&GGDMs!!}-!a%3sAv1E1Q31OP !3-cAg-rp   )r?   r  r  Nr+  )r   r  r  rY   r[   r  r/   )
rc   rd   r?   r  r  r  rf   r  r   r  s
   &f&&&     rm   r  TestKurtosis.test_vectorization  s[     ii##M2JJszz),-	.& nnQDq$>!rp   r   r  )r   r   r   r   r  r   r   r   r  r  r  r  r  r  r  r   r   r   s   @rm   r  r    s     ! [[ ST? U?>JBCI [[V%56[[VeT]3[[Xt}5" 6 4 7"rp   r  c                 ~   \        R R R7      p\        P                  ! ^^R7      pV ! \        P                  ! \        P
                  WR7      4      p. p\        P                  ! 4       ;_uu_ 4        \        P                  ! R4       \        \        VP                  4      4       F  p\        P                  ! \        4      ;_uu_ 4        \        P                   ! V^VR7      p\        P"                  ! V^ 8  4      '       dB   \        P"                  ! \        P$                  ! V4      4      '       d   VP'                  V4       RRR4       K  	  RRR4       \(        P*                  ! V4       V ! \(        P,                  P/                  V4      4      pW53#   + '       g   i     EK  ; i  + '       g   i     Lc; i)F)	allow_nanallow_infinity)min_dimsmin_side)r7   elementsr  errorrv  N)dictnpstarray_shapesarraysr   r   r\  r]  r^  r  r   r  
contextlibsuppress	Exceptionr[   rj  r  r  rI  
hypothesisassume
strategiessampled_from)drawr  r  r  ok_axesr?   r}   s   &      rm   ttest_data_axis_strategyr    s(    eE:Hq15E "**xMND G 
	 	 	"	"g&#djj/*D$$Y//ll4qt<66#'??rvvbkk#.>'?'?NN4( 0/ + 
# g 
%%227;<D: 0// 
#	"s,   1AF,A(F4FF,F)"
F,,F<	c                     a  ] tR tRt o . ROt. ROtRtRtRtRt	R t
RtRtRt]	^,          t^]	^,          ,
          t]P"                  P%                  R4      ]P"                  P%                  R4      R	 4       4       tR
 t]P"                  P%                  R4      R 4       t]! RRR7      ]P"                  P/                  R. R!O4      R 4       4       tR t]! RRR7      ]P"                  P4                  ]P8                  ! ]P:                  P=                  RR"4      ]! 4       R7      ]P"                  P/                  RRR.4      R 4       4       4       4       t Rt!V t"R# )#TestStudentTesti8  r   r   gMXz?g4/?gFX5t?r  r  c           	     f   \        4       ;_uu_ 4       p\        P                  ! R R R7      ;_uu_ 4        VP                  \        R4       \        V4      '       g   VP                  R4      MRp\        P                  ! VR4      w  rERRR4       RRR4       \        XVP                  VP                  4      4       \        XVP                  VP                  4      4       \        P                  ! VP                  V P                  4      R4      w  rE\        WAP                  V P                  4      4       \        WQP                  V P                  4      4       \        P                  ! VP                  V P                  4      R4      pR
p\        WgVR7       \        P                  ! VP                  V P                   4      R4      w  rE\        WAP                  V P"                  4      4       \        WQP                  V P$                  4      4       \        P                  ! VP                  V P                  4      R4      w  rE\        WAP                  V P&                  4      4       \        WQP                  V P(                  4      4       \        P                  ! VP                  V P                  4      R	4      w  rE\        WAP                  V P*                  4      4       \        WQP                  V P,                  4      4       R#   + '       g   i     EL; i  + '       g   i     EL; i)r}  r  divide!Degrees of freedom <= 0 for slicer   r   Nr   rd   r   r   r>  r=  )r   r   r  r   r   r)   rY   r[   ttest_1sampr0   rb   X1r/   T1_0P1_0r   X2T2_0P2_0T1_1P1_1T1_2P1_2)rc   rd   r   rK  tre  r   r@  s   &&      rm   test_onesampleTestStudentTest.test_onesampleK  s      CHX>>JJ~'JK&.rll

2A$$Q+DA ? !
 	2::bff-.2::bff-.  DGG!4b9::dii01::dii01

477 3R8,
C3  DGG!4b9::dii01::dii01  DGG!4b9::dii01::dii01  DGG!4b9::dii01::dii019 ?>> !  s#   !LAL	LL	LL0	c           
     R   \        V4      '       gj   VP                  R RRVP                  .4      pRp\        P                  ! \
        VR7      ;_uu_ 4        \        P                  ! VR RR7       RRR4       R# \        P                  P                  ^^
^3RR	7      p\        P                  V^2&   \        P                  ! R
R7      ;_uu_ 4        \        \        P                  ! VR4      \        P                  \        P                  34       \        \        P                  ! VRRR7      R4       \        \        \        P                  VRRR7       \        \        \        P                  VRRR7       RRR4       R#   + '       g   i     R# ; i  + '       g   i     R# ; i)r   r   r   %Use of `nan_policy` and `keepdims`...r   r   r   Nit r#  r$  r  r  r}  r~  r8   r   r   )g̈́^Bg/kCm?)r)   rY   rb   r   r   NotImplementedErrorr[   r  rX  r  r   r  r   r   r   r   )rc   rd   rf   r  s   &&  rm   test_onesample_nan_policy)TestStudentTest.test_onesample_nan_policym  s   ||

BB/0A=G2'BB!!!RF; CJJNNq'NJ"[[**u00C8266266:JK%e&7&736&R&QS*e&7&7CGT*e&7&7C%-/ +* CB +**s   FB'FF	F&	z+ignore:divide by zero encountered in dividec                   R p\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! VP                  V P                  4      RRR7       RRR4       \        P                  ! VP                  V P                  4      RRR7      w  r4\        WAP                  V P                  4      4       \        W1P                  V P                  4      4       \        P                  ! VP                  V P                  4      RRR7      w  r4\        WAP                  V P                  4      4       \        W1P                  V P                  4      4       R#   + '       g   i     EL; i)	8`alternative` must be 'less', 'greater', or 'two-sided'.r   r   r  r  Nr   r  r  )r   r   r   r[   r  rY   r	  r/   P1_1_lr  P1_1_g)rc   rd   r  r  re  s   &&   rm   test_1samp_alternative&TestStudentTest.test_1samp_alternative  s    L]]:W55bjj127K 6   DGG!4bfM::dkk23::dii01  DGG!4biP::dkk23::dii01 655s   3EE-		jax.numpyGeneric stdtrit mutates array.r  r  r  r  c                   \         P                  P                  R 4      p^
pVP                  VR^R7      pVP                  4       pVP	                  R4      P
                  pVP	                  WWR7      pVP	                  WgR7      pRRR.RR	\         P                  .R
\         P                  ) R./p\        P                  ! WVVR7      p	V	P                  RR7      p
\        V
P                  VP	                  W,          ^ ,          4      4       \        V
P                  VP	                  W,          ^,          4      4       \        V	P                  VP	                  V^,
          4      4       R# )l   <PleH r2   r  r#  r$  r   r6   r  gÍ]?g$(}w@r  gS1?r  g]@)popmeanr  333333?confidence_levelN)r   r  r  r  rY   r7   r!  r[   r  r  r/   r  r  r0   df)rc   rd   r  r  r  rf   r&  r7   r  r   r  s   &&&        rm   test_1samp_ci_1d TestStudentTest.test_1samp_ci_1d  s$    ii##$78JJA3aJ0**, 

3%%JJqJ&**W*2/1CD-rvv6!235 L$$d$;

3+;A+> ?@C,<Q,?!@A

1Q30rp   c                    \         P                  ! VP                  R 4      R4      pRp\        P                  ! \
        VR7      ;_uu_ 4        VP                  ^
R7       RRR4       R#   + '       g   i     R# ; i)r   r   4`confidence_level` must be a number between 0 and 1.r   r(  N)r[   r  r   r   r   r   r  )rc   rd   r   r  s   &&  rm   test_1samp_ci_iv TestStudentTest.test_1samp_ci_iv  sR    		#3H]]:W55##R#8 6555s   A**A;	Tz	Too slow.r   rD  )alpha	data_axisc                   Vw  rVVP                  V4      p\        P                  ! VR W6R7      pVP                  VR7      w  rVR8X  d   TMT	p
VP	                  WR7      p
\        P                  ! WZW6R7      p\        VP                  4      pVP                  V4       VP                  VP                  ^V,
          VP                  R7      V4      p\        VP                  V4       R# )r   r  r(  r  r>   r6   N)rY   r[   r  r  expand_dimsr:  r  r  r  r   r/   r=  )rc   r1  r2  r  rd   r  r?   r   lr  r&  r  r  s   &&&&&        rm   test_pvalue_ciTestStudentTest.test_pvalue_ci  s     
zz$b,7D&&&>"i/!Q...4;RTZZ 		$oobjj5

jCUK

C(rp   r   NrP  r   r   )r   r   r   gMXzgMXzrn  g?)#r   r   r   r   r	  r  r
  r  r  r  r  r  r  r  r  r  r   r   r   r  r  r   r   r  r+  r/  rr  r  givenr  floatsr  r6  r   r   r   s   @rm   r  r  8  sm     
B	BDDDDDDDDAXF$(^F[[ WX[[ VW2 X Y2@/( [[ MN2 O2 k*JK[[],LM1 N L109 d;7[[J1188H 8 :<[[]VY,?@) A<  8
)rp   r  c                     a  ] tR tRt o R t]P                  P                  R. RO4      R 4       t]P                  P                  R. RO4      R	 4       t	]P                  P                  R. RO4      R
 4       t
]P                  P                  R. R O4      R 4       t]P                  P                  R. RO4      R 4       t]P                  P                  R. RO4      R 4       t]P                  P                  R. R O4      R 4       t]P                  P                  RR. R!O3R. R"O3R. R#O3R. R!O3.4      R 4       t]P                  P                  RR. R$O3R. R%O3R. R&O3R. R$O3.4      R 4       tR. ^]P$                  3R]P$                  .^]P$                  3R]P$                  .. R'O]P$                  ]P$                  ]P$                  .3R^^.^^]P$                  .^2^d]P$                  .3R^^]P$                  .. R'O. R(O3R^^.^ ^]P$                  .^ ^2]P$                  .3R]P$                  ]P$                  .. R'O]P$                  ]P$                  ]P$                  .3.t]P                  P                  R]4      R 4       tR^^^]P$                  .. R)OR3R. R)O^^^]P$                  .R3.t]P                  P                  R]4      R 4       t]P                  P                  R. R*O4      R 4       tRtV tR# )+TestPercentileOfScorei  c                .    \         P                  ! V/ VB # r  )r[   percentileofscore)rc   argskwargss   &*,rm   fTestPercentileOfScore.f  s    &&777rp   zkind, resultr  r^   strictweakc                J    . ROp\        V P                  V^VR7      V4       R# )rW   kindN
rW   rE   r   r   rw   rz   rJ   rF   rI   rO   r   rA  rc   rG  r  rK  s   &&& rm   test_unique!TestPercentileOfScore.test_unique  s"    
 ,TVVAqtV,f5rp   c                J    . ROp\        V P                  V^VR7      V4       R# )rW   rF  N)
rW   rE   r   r   r   rw   rz   rJ   rF   rI   rI  rJ  s   &&& rm   test_multiple2$TestPercentileOfScore.test_multiple2  "    
 +TVVAqtV,f5rp   c                J    . ROp\        V P                  V^VR7      V4       R# )rW   rF  N)
rW   rE   r   r   r   r   rw   rz   rJ   rF   rI  rJ  s   &&& rm   test_multiple3$TestPercentileOfScore.test_multiple3  rP  rp   c                J    . ROp\        V P                  V^VR7      V4       R# )rW   rF  N)
rW   rE   r   rw   rz   rJ   rF   rI   rO   rP   rI  rJ  s   &&& rm   test_missing"TestPercentileOfScore.test_missing  s"    
 -TVVAqtV,f5rp   c                J    . ROp\        V P                  V^(VR7      V4       R# )rO   rF  N
rO   r  r  r  r  rD  F   rH  r!  r  rI  rJ  s   &&& rm   r8  (TestPercentileOfScore.test_large_numbers  s"    
 6TVVArV-v6rp   c                J    . ROp\        V P                  V^(VR7      V4       R# )rO   rF  N)
rO   r  r  r  r  r  r  rD  rY  rH  rI  rJ  s   &&& rm   test_large_numbers_multiple32TestPercentileOfScore.test_large_numbers_multiple3  s"    
 5TVVArV-v6rp   c                J    . ROp\        V P                  V^(VR7      V4       R# )rO   rF  N
rO   r  r  r  rD  rY  rH  r!  r  n   rI  rJ  s   &&& rm   test_large_numbers_missing0TestPercentileOfScore.test_large_numbers_missing  s"    
 7TVVArV-v6rp   c                N    . ROp\        V P                  V. ROVR7      V4       R# )rO   rF  Nr_  )ry   rO   r`     rI  rJ  s   &&& rm   test_boundaries%TestPercentileOfScore.test_boundaries  s#    
 7TVVA0tV<fErp   c           
         ^^^^^^^^^	\         P                  5.
p\        V P                  V\         P                  ) ^\         P                  5.VR7      V4       R# )rW   rF  N)r   r!  r   rA  rJ  s   &&& rm   test_infTestPercentileOfScore.test_inf  sP    
 1aAq!Q0TVVARVVG44V@&Irp   r  r   zpolicy, a, score, resultc                @    \        V P                  W#VR 7      V4       R# )r   NrI  )rc   policyrK  r  r  s   &&&&&rm   test_nans_ok"TestPercentileOfScore.test_nans_ok  s    TVVAV8&Arp   r   r   zpolicy, a, score, messagec                    \        \        VR 7      ;_uu_ 4        V P                  W#VR7       RRR4       R#   + '       g   i     R# ; i)r   r   N)r   r   rA  )rc   rk  rK  r  r  s   &&&&&rm   test_nans_fail$TestPercentileOfScore.test_nans_fail&  s.    :W55FF1F/ 6555s	   8A		r  c                    \         P                  ! . RO4      pVP                  V4      pV^
,          p. ROp\        V P	                  W#RR7      V4       R# )ry   r  rF  N)ry   rW   rE   r   r   rw   rH  )r   r   r]   r   rA  )rc   r  rK  ry  resultss   &&   rm   test_ndTestPercentileOfScore.test_nd+  sF     HH'(5!)+TVVAFV3W=rp   r   N))r  r  )r^   #   rC  r  )rD  r  ))r  r  )r^   r  rv  )rD  r  ))r  r  )r^   r  rv  )rD  rD  ))r  r  )r^   r  rv  )rD  r  )ry   rO   r  r  )ry   rw   _   r  )ry   ry   r!  r  )ry   rO   r  )ry   rw   rw  )ry   ry   r!  r  )ry   r  r  r  ))rz   rW  rE   rW   r   )rE   rW   rW   r   )r   r   r   r   rA  r   r   r  rK  rN  rR  rU  r8  r\  ra  re  rh  r   rb   casesrl  ro  rs  r   r   r   s   @rm   r<  r<    si    8 [[^ .< =6	=6 [[^ .< =6	=6 [[^ .< =6	=6 [[^ .< =6	=6 [[^ .< =7	=7 [[^ .< =7	=7 [[^ .< =7	=7 [[^v7H.I/5.G/7.I/57H.I.K LF	LF [[^v|.D/5z.B/7.D/5|.D.F GJ	GJ 2q"&&)BFF8Q/BFF8Y0HIAq6Aq"&&>BRVV3DEq!RVVni>q!fq!RVVnq"bffo>rvvrvv&	BFFBFFBFF3KLNE [[7?B @B 
1aBFF#Y	(	*	)aArvv.	(	*E [[8%@0 A0 [[W ' >>rp   r<  Caser?   )f_obsf_exprN  r?   chi2r  mod_logcrc                   P  a  ] tR tRt o R t]P                  P                  R]4      ]P                  P                  R. RO4      R 4       4       t	R t
R t]P                  P                  R]4      ]P                  P                  R. RO4      R	 4       4       tR
 tR tR tRtV tR# )TestPowerDivergenceix  c           
     d   VP                  R 4      P                  pVP                  WR7      pVe   VP                  W(R7      MTpVf   \        V4      p	M2Ve   VP                  W4      MV3p
V
^ ,          P                  V,          p	\        4       ;_uu_ 4       pVP                  \        R4       \        P                  ! WVWER7      w  r\        WP                  WhR7      4       V^8X  g   VR8X  d7   \        P                  ! WVVR7      w  r\        WP                  WhR7      4       RRR4       \        P                   ! V4      p\        P                  P                  P                  VV	^,
          V,
          4      p\        XVP                  WR7      4       R#   + '       g   i     L|; i)r   r6   Nr  r|  rN  r?   lambda_pearson)r|  rN  r?   )rY   r7   r,   broadcast_arraysr  r   r   r   r[   power_divergencer/   	chisquarer   distributionsr}  sf)rc   r{  r|  rN  r?   r  expected_statrd   r7   num_obsr  r   statre  
expected_ps   &&&&&&&&       rm   check_power_divergence*TestPowerDivergence.check_power_divergence{  sX   

2$$

5
.272C

5
.<enG;@;Lb))%7!8 Qiood+G  CJJ~'<=,, %%)<GD D**]*"HI!|w)3//%4/35jjj&LM ! zz$((--00181t1CE
2::j:>?! ! s   BFF/	caselambda_statNc           	         Vw  rE\        W4      pV P                  VP                  VP                  VP                  VP
                  WFV4       R # r  )rj  r  r{  r|  rN  r?   rc   r  r  rd   r  attrr  s   &&&&   rm   rX  TestPowerDivergence.test_basic  sA     $+##DJJ

DIItyy$+B	@rp   c           
        \         ^ ,          p\         ^,          p\        P                  ! VP                  VP                  34      p\        P                  ! \        P                  ! VP                  4      \        P
                  ! VP                  4      ,          VP                  34      pVP                  V4      pVe   VP                  V4      MTpV P                  WE^ ^RVP                  VP                  .VR7       V P                  WE^ ^RVP                  VP                  .VR7       V P                  WE^ ^RVP                  VP                  .VR7       V P                  WE^ ^RVP                  VP                  .VR7       VP                  VP                  VP                  4      R4      pV P                  VR^ RRVP                  VR7       R# )ry   Nr  r  log-likelihoodmod-log-likelihoodcressie-readr;  )power_div_1d_casesr   vstackr{  	ones_liker^   r|  rY   r  r}  r  r~  r  r]   )rc   rd   case0case1r{  r|  f_obs_reshapes   &&     rm   r  TestPowerDivergence.test_axis  s   "1%"1%		5;;45		2<<4RWWU[[5II ;;( ) 

5!%*%6

5!E##Q5::uzz2r 	$ 	; 	##Q%))UYY!7B 	$ 	@ 	##Q#emmU]]%C 	$ 	L 	##Q%((3 	$ 	<
 

2::ekk#:FC##dAt%** 	$ 	-rp   c                   \         ^ ,          p\         ^,          p\        P                  ! VP                  VP                  34      P                  p\        P                  ! \        P
                  ! VP                  4      \        P                  ! VP                  4      ,          VP                  34      P                  pVP                  VP                  .pVP                  R4      P                  pVP                  WGR7      pVP                  WWR7      pVP                  WgR7      pVP                  ^ .^..4      p\        P                  ! WEVR7      w  r\        W4       \        P                  ! WEVR,          R7      w  r\        P                  ! WEVR,          R7      w  rVP                  WP                  R3,          WP                  R3,          3^ R7      p\        W4       R# )	ry   r   r6   rM  r   r>   Nr  r  )r  r   r  r{  r   r  r^   r|  r}  rY   r7   r[   r  r/   r  rn  )rc   rd   r  r  r{  r|  expected_chi2r7   rN  r  re  r  p0p1r  s   &&             rm   test_ddof_broadcasting*TestPowerDivergence.test_ddof_broadcasting  sn    #1%"1%		5;;4577		2<<4RWWU[[5II ;;( ))* 	 UZZ0

2$$

5
.

5
.

=
> zzA3*%((DA, &&u$t*E&&u$t*EYY::q= 12jj!m3DEAYN
&rp   c                   Vw  rE\        W4      p\        P                  ! 4       ;_uu_ 4        V P                  VP                  VP
                  VP                  VP                  WFV4       R R R 4       R #   + '       g   i     R # ; ir  )rj  r\  r]  r  r{  r|  rN  r?   r  s   &&&&   rm   test_empty_cases$TestPowerDivergence.test_empty_cases  s_     $+$$&&''

DJJ		499, '&&&s   ?A66B	c                j   \         ^ ,          P                  p\         ^ ,          P                  p\         ^ ,          P                  p\         ^ ,          P                  pVP                  R4      P                  pVP                  W&R7      p\        P                  ! W#VVRR7      pRp\        WxVR7       R# )ry   r   r6   r  r  r  Nr  )
r  r{  r|  rN  r?   rY   r7   r[   r  r   )	rc   rd   r{  r|  rN  r?   r7   r   r@  s	   &&       rm   'test_power_divergence_result_attributes;TestPowerDivergence.test_power_divergence_result_attributes  s    "1%++"1%++!!$))!!$))

2$$

5
. $$Ud*.	C,
C3rp   c           	        VP                  R R.RR..4      pVP                  RR.RR..4      pRp\        P                  ! \        VR7      ;_uu_ 4        \        P
                  ! W!P                  RR	.4      R
7       RRR4       \        P                  ! \        VR7      ;_uu_ 4        \        P
                  ! W#^R7       RRR4       \        P
                  ! W#R
7      w  rV\        WQP                  RR.4      4       \        WaP                  RR.4      4       R#   + '       g   i     L; i  + '       g   i     Lv; i)r   r2        >@r8   rW  g     A@g      9@For each axis slice...r         N@r|  N)r|  r?   g̑m@gUUU@gj^4;?g4;?)rY   r   r   r   r[   r  r/   )rc   rd   r{  r|  r  r  r  s   &&     rm   test_power_divergence_gh_122822TestPowerDivergence.test_power_divergence_gh_12282   s    

S#Jc
34

RISz23*]]:W55""5

C:0FG 6]]:W55""5A> 6++E?
jj*j)ABCjj*j)ABC 6555s   )D*D1D.	1E	c           	     v   VP                  . RO4      pR pVP                  RVP                  ^ ,          R,           4      pVP                  VP	                  V4      VP	                  VP                  W4,          4      4      ,          4      pVP                  WSV,          ,           4      pVP                  W!P                  R3,          WaP                  R3,          34      P                  pVP                  . R!NRNR"NRNR#NRNR$NR
NR%NRNR&NRNR'NRNRNRNRNRNRNRNRNRNRNRNR	NRNRNRNRNRNRNRN4      pVP                  VR(4      p\        VP                  ^ ,          4       FL  pW^ 3,          W^3,          r\        P                  ! VR),          VR*,          V	R7      w  r\        WRR7       KN  	  R# )+rW  r8   r   r   r   r   g    @g     r@gffffffP@r   gLD@r2   g      A@g     =@r1   g     :@r   g8@gffffff7@gq=
ףp?g7@g333336@g6@gfffff6@g8@g     A@g     j@)r  g{Gzt?r  N)rW  r        ,@g      1@r8   r  r   r   r   r   r   r   r  r   r   r   r   r   g*kqg      $r~  r  g       rp  rP  ro  )rU   rE   r  )r   rW   )rY   r   r  r  r^  expr  rn  r   r]   r  r[   r  r/   )rc   rd   obsbetar  r1  expected_countstable4table5r  r  r  re  s   &&           rm   /test_power_divergence_against_cressie_read_dataCTestPowerDivergence.test_power_divergence_against_cressie_read_data  sm    jj @ AIIb#))A,+,rvvc{RVVBFF46N%;;<&&a0 C

A.+JJM:< ==>Q 	     	 	
 
                       !  !" #" # & FG,v||A'A%+qD\6Q$<],,VC[&+5<>GDDd;	 (rp   r   ))Nr}  r  r}  )rW   r}  r  r  r  r~  r  r  rH  r  )r  r  r  r  r  )r   r   r   r   r  r   r   r  r  rX  r  r  power_div_empty_casesr  r  r  r  r   r   r   s   @rm   r  r  x  s     @@ [[V%78[[]	./@	/ 9
@-: 'D [[V%:;[[]	./,	/ <
,4D-< -<rp   r  c                   t   a  ] tR tRt o R tR t]P                  P                  RRR	.4      R 4       t	Rt
V tR# )
TestChisquarei=  c                    \        \        R R7      ;_uu_ 4        VP                  RR.4      pVP                  RR.4      p\        P                  ! W#R7       RRR4       R#   + '       g   i     R# ; i)r  r   r   r2  r  r  r  N)r   r   rY   r[   r  )rc   rd   r{  r|  s   &&  rm   test_chisquare_12282a#TestChisquare.test_chisquare_12282a?  sR     :-EFFJJSz*EJJSz*EOOE/ GFFFs   >A""A3	c                J   \         P                  P                  R 4      p^
pVP                  RRVR7      pVP	                  V4      pVP                  V4      pVP                  WTP                  R7      p\        P                  ! WTRRR7      pWT,
          VP                  V4      ,          pVP                  V^,          4      p\        VP                  V4       \        VP                  W8P                  R7      4      p	\        VP                  V	P                  V4      4       R# )	l   *m{m r  r9  r  r6   F)r|  rN  	sum_checkNrU   )r   r  r  r  poissonrY   r7   r[   r  rH  r^  r/   r>  r#   r=  r  )
rc   rd   r  r  lamrf   r   r,  r>  r  s
   &&        rm   test_chisquare_12282b#TestChisquare.test_chisquare_12282bH  s     ii##$45kk$1k-KKjjoJJq		J*ooauEW$FF1a4L	y1A__=>

BEE)$45rp   zn, dtypec           	        \        W24      pVP                  V^ .VR7      pVP                  V^,          V^,          .VR7      p\        P                  ! WE4      pVw  rx\	        WsP                  WP                  R4      P
                  R7      RR7       \        VP                  V4       \        VP                  V4       R# )ry   r6   r   vIh%<=r  N)	rj  rY   r[   r  r/   r7   r0   r>  r=  )	rc   r  r7   rd   r  r  r   r  re  s	   &&&&     rm   #test_chiquare_data_types_attributes1TestChisquare.test_chiquare_data_types_attributes[  s     "jj!Quj-jj!q&!q&)j7ooc'jj**R.2F2FjGeTt,

A&rp   r   N)rd  r%  )i@B r  )r   r   r   r   r  r  r   r   r  r  r   r   r   s   @rm   r  r  =  s;     06& [[Z.:L)MN
' O
'rp   r  c            	         \        . RO4      \        . RO4      \        . RO4      \        . RO4      .p \        . RO4      \        . RO4      \        . RO4      \        . R	O4      .p\        . R
O4      \        . RO4      \        . RO4      \        . RO4      .p\        \        P                  ! V ^ ,          V ^,          V ^,          V ^,          4      R4       \        \        P                  ! V^ ,          V^,          V^,          V^,          4      R4       \        \        P                  ! V^ ,          V^,          V^,          V^,          4      R4       \	        \
        \        P                  V^ ,          V^,          4       Rp\        P                  ! V !  p\        WC4       \        \        P                  ! V ^ ,          V ^,          V ^,          V ^,          4      R4       \        \        P                  ! V^ ,          V^,          V^,          V^,          4      R4       \	        \
        \        P                  V^ ,          V^,          4       R# )"~j?N)r  g^I+?gI+?gjt?gMbX9?gʡE?x&?-?g?r   Gz?g+?gv?g9v?)g~jt?gx?gOn?r  g"~j?n?gK7A`?r  g7A`?r   bX9?gZd;O?g1Zd?gK?)gy&1?gzG?g`"?g!rh?g'1Z?gZd;O?grh|?gjt?gʡE?r   gzG?gS?gJ4?gʡE?)gK7?gh|?5?gl?g/$?g#~j?r  gQ?      ?g      ?r   r  g rh?g333333?
ףp=
?)r   r   rw   r   rw   r   rE   rw   r   r   r   r   )rE   rE   rW   rE   r   rW   rE   r   rE   rW   rW   r   )rE   r   r   r   r   r   r   r   r   rW   rE   rW   )r   rw   r   r   r   r   r   r   r   r   r   r   )r   g#@      !@r   g$@)g333333@g@g@r  g@)r  r  rB   r   @)g!@g!@333333 @ffffff
@g333333"@)gNt$@gBv?)g
__2@g5"]i2?)g\(\%@g+ԋ?r  )r   r   r[   friedmanchisquarer   r   r   r{  )r  r  r  r@  r   s        rm   test_friedmanchisquarer  i  s   
  8 9
 9 :
 : ;
 9 :
;B )
*
)
*
)
*
)
*
,B &
'
%
&
%
&
%
&
(B
 e55beBqE"Q%1NDFe55beBqE"Q%1NFHe55beBqE"Q%1N9;*e55beBqEB )J

!
!2
&C( f66r!ube79!ubeEDF f66r!ube79!ubeE9; *f66r!uRUCrp   c                   J   a  ] tR tRt o RtR
R ltR
R ltR tR tR t	Rt
V tR	# )
TestKSTesti  zLTests kstest and ks_1samp agree with K-S various sizes, alternatives, modes.c                    \         P                  ! VR W%R7      p\        P                  ! W4.4      p\	        \        P                  ! V4      WR7       R# rX  r  r  rW  N)r[   kstestr   r   r   	rc   rf   r  expected_statisticexpected_probr  r  r  r  s	   &&&&&&&  rm   _testOneTestKSTest._testOne  s9    a[L88/?@!"((6"2HNrp   c                    \         P                  ! VR W#R7      p\         P                  ! V\         P                  P                  W#R7      p\        \        P                  ! V4      WdR7       R# r  )r[   r  ks_1samprX  cdfr   r   r   )rc   rf   r  r  r  r  result_1samps   &&&&&  rm   _test_kstest_and_ks1samp#TestKSTest._test_kstest_and_ks1samp  sE    a[L~~a2=J!"((6"2LRrp   c                ~    \         P                  ! R^^	4      pRp\        P                  ! VR4      p\	        W24       R# )rW   rX  NrU   r  )r   r5  r[   r  r   rc   rf   r@  r   s   &   rm   test_namedtuple_attributes%TestKSTest.test_namedtuple_attributes  s1    KKAq!,
ll1f%C,rp   c                *   \         P                  ! R^^	4      pV P                  VR4       \         P                  ! R^^	4      pV P                  VR4       . R	OpV P                  VR4       V P                  VRRR7       V P                  VRRR7       R# )
rW   r  r  r  r  r  NrU   
r  Q?g333333g(\?Q?g(\ſg{GzgHzG?g\(\gGz)r   r5  r  r  s   & rm   test_agree_with_ks_1samp#TestKSTest.test_agree_with_ks_1samp  s    KKAq!%%a5KKR#%%a5N%%a5%%a%A%%ag%>rp   c                &   \         P                  ) ^ ^\         P                  .p\        P                  ! V\        P                  P
                  4      p\        P                  ! V\        P                  P
                  RR7      p\         P                  ! \         P                  ! V4      4      '       g   Q h\        W#4       \         P                  ! VP                  4      '       d   Q h\         P                  ! VP                  4      '       d   Q hR# )ry   T)_no_decoN)r   r!  r[   r  cauchyr  r  r  r   rw  r>  r=  )rc   r  r   r  s   &   rm   test_pm_inf_gh20386TestKSTest.test_pm_inf_gh20386  s     Arvv&ll4!1!12ll4!1!1DAvvbkk#&''''S88CMM****88CJJ'''''rp   r   NautorM   )r   r   r   r   r5  r  r  r  r  r  r   r   r   s   @rm   r  r    s(     VOS-
?	( 	(rp   r  c                      a  ] tR tRt o RtRR ltR tR tR tR t	]
P                  P                  R]P                  ]P                  .4      ]
P                  P                  R	. RO4      R
 4       4       tRtV tR# )TestKSOneSamplei  zQ
Tests kstest and ks_samp 1-samples with K-S various sizes, alternatives, modes.
c                    \         P                  ! V\         P                  P                  W%R 7      p\        P
                  ! W4.4      p\        \        P
                  ! V4      WR7       R# )r  rW  N)r[   r  rX  r  r   r   r   r  s	   &&&&&&&  rm   r  TestKSOneSample._testOne  sA    5::>>{V88/?@!"((6"2HNrp   c                    \         P                  ! R^^	4      pRp\        P                  ! V\        P                  P
                  4      p\        W24       R# )rW   NrU   r  )r   r5  r[   r  rX  r  r   r  s   &   rm   r  *TestKSOneSample.test_namedtuple_attributes  s9    KKAq!,
nnQ

/C,rp   c                >   \         P                  ! R^^	4      pV P                  VRRR4       \         P                  ! R^^	4      pV P                  VRRR4       . ROpV P                  VRRR4       V P                  VRRR	R
R7       V P                  VRRRR
R7       R# )rW   r  g|N?g7.s?g{CTp?g M<b*?gZL?g86J4?r  g+?r  r  r  gHD?gr?NrU   r  r  r   r5  r  r  s   & rm   test_agree_with_r!TestKSOneSample.test_agree_with_r  s    KKAq!a&9;NOKKR#a&9;OPNa&79JKa$57HwWa!24EGTrp   c                    \         P                  P                  R ^dRR7      pV P                  VRRRRR7       V P                  VRRR	4       V P                  VR
RR4       R# )r4  h:)r#  r  r  r  ghх?g7?asympr  r  g^h?r  gv!ԉ}?g*z)?N)r[   rX  r  r  r  s   & rm   test_known_examples#TestKSOneSample.test_known_examples  s`    JJNNs9NEa&9;O" 	 	$a!46JKa$9;NOrp   c           	        \        \        P                  ! \        \        P                  ^R4      4      4       \        \        RR7      ;_uu_ 4        \        R^R4       RRR4       \        \        P                  ! \        R^R4      4      4       \        P                  ! . RO4      p\        \        VR	^4      P                  \        \        \        .R7       R#   + '       g   i     L; i)
rW   Tzn is not integral: 1.5r   r2   N)dtypesrU   ))rC  rW   Tr   )rC  皙?Tr   )rC  ry   Tr   )rC  gTr   )          ?Tr   )r  r  Fr   )r  r1   Tgb?)r  r1   FgiNq>)r        ?Tgv(?)r        ?TgT	?)@  g\(\?Fr   )r        ?Fg(>)r  gQ?Fg@c?)r        ?FgX+ʳP?r  )r   r   rw  r   rb   r   r   rY   r   checkintr  bool)rc   datasets   & rm   test_ks1samp_allpaths%TestKSOneSample.test_ks1samp_allpaths  s    D123:-EFFCD! GQ-./** 
 4 	'9a066sE4>P6Q= GFs   CC-	ksfunc*alternative, x6val, ref_location, ref_signc                   \         P                  ! ^
4      R,           pW6^&   \        P                  ! ^
R7      P                  pV! WgVR7      p\        VP                  RRR7       VP                  V8X  g   Q hVP                  V8X  g   Q hR# )rO   r1   rb  r  rD  rD  r  N)	r   r   r[   r  r  r
   r>  statistic_locationstatistic_sign)	rc   r&  r  x6valref_locationref_signrf   r  r   s	   &&&&&&   rm   test_location_sign"TestKSOneSample.test_location_sign  su     IIbMC!mm"%))Q5s7%%555!!X---rp   r   Nr  ))r  rz   rz   rW   )r  rJ   rJ   rU   )r  rz   rz   rW   )r  rJ   rJ   rU   )r   r   r   r   r5  r  r  r  r  r$  r   r   r  r[   r  r  r.  r   r   r   s   @rm   r  r    sz     O-UP!RF [[Xenn'EF[[I78

.8 G
.rp   r  c                     a  ] tR tRt o RtRR ltR tR tR tR t	R t
R	 tR
 t]P                  P                  R 4       t]P                  P                  R 4       tR tR t]P                  P(                  R 4       t]P                  P(                  R 4       t]P                  P                  R 4       tR t]P                  P                  R 4       t]P                  P5                  R. ^.3^.. 3. . 334      R 4       t]P                  P(                  R 4       tR t]P                  P5                  R]P>                  ]P@                  .4      ]P                  P5                  R. RO4      R 4       4       t!Rt"V t#R# )TestKSTwoSamplesi/  z<Tests 2-samples with K-S various sizes, alternatives, modes.c                    \         P                  ! WW6R 7      p\        P                  ! WE.4      p\	        \        P                  ! V4      V4       R# )r  N)r[   ks_2sampr   r   r   )	rc   r  r  r  r  r  r  r  r  s	   &&&&&&&  rm   r  TestKSTwoSamples._testOne2  s7    ?88/?@!"((6"2H=rp   c                   V P                  ^ .^.RRR4       V P                  ^ .^.RRR4       V P                  ^ .^.RRR4       V P                  ^.^ .RRR4       V P                  ^.^ .RRR4       V P                  ^.^ .RRR4       R# )ry   r  r   r  r1   r  r   N)r  r|  s   &rm   	testSmallTestKSTwoSamples.testSmall8  s    qcA3UC8qcA3	5#6qcA3s3qcA3UC8qcA3	5#6qcA3s3rp   c                z   \         P                  ! R R.4      pVR,           pVR,
          p\         P                  ! . R
O4      pV P                  W$RRR 4       V P                  W$RRR4       V P                  W$RRR4       V P                  W4RRR4       V P                  W4RRR4       V P                  W4R^ R 4       R	# )r   r   r  r  r  rE  r  ro  rG  Nr  rV  rH  r   r   r  rc   r  data1pdata1mr  s   &    rm   testTwoVsThreeTestKSTwoSamples.testTwoVsThree@  s    #s$)f['3?fY=fVWc:f['3?fY=fVQ4rp   c                z   \         P                  ! R R.4      pVR,           pVR,
          p\         P                  ! . RO4      pV P                  W$RRR	4       V P                  W$RRR
4       V P                  W$RRR4       V P                  W4RRR4       V P                  W4RRR4       V P                  W4R^ R 4       R# )r   r   r  r  r  r  NrD  r1   g?g?r  皙?r  rn  r4  r9  r:  s   &    rm   testTwoVsFourTestKSTwoSamples.testTwoVsFourL  s    #s$-.f['7CfY@fVWg>f['6BfY@fVQ4rp   c                f   \         P                  ! ^^d^d4      pV^,           R,           pV^,           R,
          pV P                  WRR
R4       V P                  WRR
R4       V P                  WR^ R4       V P                  WRRR4       V P                  WRRR4       V P                  WR^ R4       R	# )rW   rD  r  g~z?r  gz;.B?r  r   gn2IU?Nr  {Gz?r  )rc   x100	x100_2_p1	x100_2_m1s   &   rm   test100_100TestKSTwoSamples.test100_100Y  s    {{1c3'1HsN	1HsN	d{I?QRdy)=OPdvq#6d{IsCdy)=NOdvq#6rp   c                   \         P                  ! ^^d^d4      p\         P                  ! ^^d^n4      pV^,           R,           pV^,           R,
          pV P                  WRRR4       V P                  WRRR4       V P                  WR^ ^4       V P                  WRRR4       V P                  WRRR4       V P                  WRR	R
4       R# )rW   rD  r  g@߿?r  g}n?r  g]O);?gѫ);?r   r   Ng?g:[?r  )rc   rE  x110
x110_20_p1
x110_20_m1s   &    rm   test100_110TestKSTwoSamples.test100_110d  s    {{1c3'{{1c3'BY_
BY_
d\CWXd	<AUVd15d\CWXd	<AUVdS9rp   c                   \         P                  ! ^.^,          ^.^,          ,           ^.^,          ,           ^.^,          ,           \        R7      pV^,           p\         P                  ! ^.^,          ^.^,          ,           ^.^
,          ,           ^.^,          ,           \        R7      p\         P                  ! ^.^
,          ^.^,          ,           ^.^
,          ,           ^.^,          ,           \        R7      pV P                  WRRR4       V P                  WRRR4       V P                  WRRR4       V P                  W4RRR	4       V P                  W4RRR
4       V P                  W4RRR4       R# )rE   r6   r  g^dH?r  gQl6y?r  r   r   g(f^?g!?g+ ϖ?Ng      ?gVdEVdE?gii?)r   r   r!  r  )rc   x2233x3344x2356x3467s   &    rm   testRepeatedValues#TestKSTwoSamples.testRepeatedValuesq  s!   !qA37*aS1W4sQw>cJ	!qA37*aS2X5a?sK!rQC!G+qcBh6!q@LeK9KLeIv7JKeFFC8eK>PQeI{<NOeFJ8JKrp   c                   \         P                  ! . RO4      pV P                  W^,           RR	R 4       V P                  W^,           RR	R4       V P                  W^,           RRR 4       V P                  WR,           RR	R 4       V P                  WR,           RR	R4       V P                  WR,           RRR 4       V P                  WR,
          RR	R 4       V P                  WR,
          RRR 4       V P                  WR,
          RR	R4       R# )
r   r  r  r  r  r   r1   Nr  rV  r9  )rc   r  s   & rm   testEqualSizesTestKSTwoSamples.testEqualSizes}  s    )e1Wk5#>e1Wi=e1WfeR8e3YUC@e3Y	5$?e3Yr:e3YUC@e3Y	5#>e3Yt<rp   c                    R Rr!RV,          V,          ^,          ^,          p\         P                  ! ^^V4      V,
          p\         P                  ! ^^V4      pV P                  WERRV,          V,          RRR7       V P                  WERRV,          V,          RRR7       V P                  WERRV,          V,          R	RR7       V P                  WER
RV,          V,          RRR7       \        4       ;_uu_ 4       pRpVP	                  \
        V4       V P                  WERRV,          V,          R	RR7       V P                  WER
RV,          V,          RRR7       RRR4       \        P                  ! RR7      ;_uu_ 4       p\        P                  ! R4       V P                  WER
RV,          V,          RRR7       \        V\
        ^4       RRR4       R#   + '       g   i     L; i  + '       g   i     R# ; i)r!  iX  r   r  g     @@r  r  r  r  g2JE?r  g     @@gsW\nc?)ks_2samp: Exact calculation unsuccessful.r  NTrX  rY  
r   r5  r  r   r   r   r\  r]  r^  r  	rc   n1n2deltarf   rg   r   r  r  s	   &        rm   testMiddlingBoth!TestKSTwoSamples.testMiddlingBoth  s    cBBr	!AKK3#e+KK3#aK"r)93! 	 	#aK"r)93" 	 	$aIv{R'79K" 	 	$aFEBJO5G" 	 	$  CAGJJ~w/MM!	6B;+;=O&  (MM!
R9K&  ( ! $$D11Q!!(+MM!
R9K&  (A~q1	 21 !  211   ;A!GAG,G)	,G=	c                    R Rr!RV,          V,          ^,          ^,          p\         P                  ! ^^V4      V,
          p\         P                  ! ^^V4      pV P                  WERRV,          V,          RRR7       V P                  WERRV,          V,          RRR7       V P                  WERRV,          V,          R	RR7       V P                  WER
RV,          V,          RRR7       \        4       ;_uu_ 4       pRpVP	                  \
        V4       V P                  WERRV,          V,          R	RR7       V P                  WER
RV,          V,          RRR7       RRR4       \        P                  ! RR7      ;_uu_ 4       p\        P                  ! R4       V P                  WER
RV,          V,          RRR7       \        V\
        ^4       RRR4       R#   + '       g   i     L; i  + '       g   i     R# ; i)r  L  r   r  g     ȹ@r  r  r  r  gZ?r  g     @@g@J?r[  r  NTrX  rY  r\  r]  s	   &        rm   testMediumBothTestKSTwoSamples.testMediumBoth  s    tBBr	!AKK3#e+KK3#aK"r)93" 	 	$aK"r)93! 	 	#aIv{R'79K" 	 	$aFFRK"$46H" 	 	$   CAGJJ~w/MM!	6B;+;=O&  (MM!b(8:L&  ( ! $$D11Q!!(+MM!b(8:L&  (A~q1	 21 !  211rc  c                j   R ^nr!VR,          pRV,          V,          ^,          ^,          p\         P                  ! ^^V4      V,
          p\         P                  ! ^^dV4      pV P                  WVRRV,          R4       V P                  WVRRV,          R4       V P                  WVR	RV,          R
4       R# )'  r  r   r  g    `@g      <r  g     @g򼉷?r  gimb:Nr  )rc   r^  r_  lcmr`  rf   rg   s   &      rm   	testLargeTestKSTwoSamples.testLarge  s    BgBr	!AKK3#e+KK3#aK38NOaIus{4GHaFGcM3IJrp   c           	         \         P                  P                  R 4      pVP                  RR7      pVP                  RR7      R,          pV P	                  W#RRRRR	7       V P	                  W#RRRR
R	7       R# )@ i  r  i  r2   r  gC?      <r  r  r  Nr   r  r  r  r  rc   r  rf   rg   s   &   rm   test_gh11184TestKSTwoSamples.test_gh11184  sw    ii##F+JJDJ!JJDJ!C'aK)<>T" 	 	$aK)<>T" 	 	$rp   c           	     J   \         P                  P                  R 4      pVP                  RR7      pVP                  RR7      R,          pV P	                  W#RRRRR	7       V P	                  W#RRR
RR	7       V P	                  W#RRRRR	7       V P	                  W#RRRRR	7       R# )rn  ri  r  i'  r2   r  g 	_r!?gAD5r  r  ro  r  r  gלN#y7r  gvqw?Nrp  rq  s   &   rm   test_gh11184_bigger$TestKSTwoSamples.test_gh11184_bigger  s     ii##F+JJEJ"JJEJ"S(aK)<>T" 	 	$aK)<>T" 	 	$aI':<R" 	 	$aF$79O" 	 	$rp   c                   \         P                  P                  R 4      p\        RRR4       F  pVP	                  VR7      pVP	                  V^
,           RR7      p\
        P                  ! W4RR7      P                  p\
        P                  ! W4RR7      P                  p\        V^V,          4       \        V^V,          4       K  	  R	# )
rn  r  i.  r  r1   r  r#  r  r  r  N)	r   r  r  r  r  r[   r3  r=  r   )rc   r  rf   vals1vals2r  r  s   &      rm   test_gh12999TestKSTwoSamples.test_gh12999  s    ii##F+tUD)AJJQJ(EJJQV#J6ENN5g>EEENN5g>EEEeQY/eQY/ *rp   c                   R Rr!VR,          pRV,          V,          ^,          ^,          p\         P                  ! ^^V4      V,
          p\         P                  ! ^^V4      pV P                  WVRRV,          RRR7       V P                  WVRRV,          R	R
R7       V P                  WVRRV,          RRR7       V P                  WVRRV,          R4       V P                  WVRRV,          R4       \        4       ;_uu_ 4       pRpVP	                  \
        V4       V P                  WVRRV,          RR
R7       V P                  WVRRV,          RR
R7       RRR4       R#   + '       g   i     R# ; i)ri  i*  r  r   r  g     @gkHY?r  r  gLɔ.?r  r  r  g.LbG2?r  r   gr?֎?r[  N)r   r5  r  r   r   r   )	rc   r^  r_  rj  r`  rf   rg   r   r  s	   &        rm   testLargeBothTestKSTwoSamples.testLargeBoth  sR    BgBr	!AKK3#e+KK3#aK6H" 	 	$aK6H" 	 	$aK6H! 	 	#aIus{4FGaFD3J0BC  CAGJJ~w/MM!	53;8J&  (MM!s
4F&  ( !   s   AEE/	c                T    Rp\         P                  ! ^^.^.4      p\        W!4       R# r>  Nr  )r[   r3  r   rc   r@  r   s   &  rm   testNamedAttributes$TestKSTwoSamples.testNamedAttributes
  s%    ,
nnaVaS)C,rp   c           
     
   ^ RI HpHp V! ^^^^4       V! R^^R4       \        P                  ! RR7      ;_uu_ 4        \        \        VRR^^4       \        \        VRR^^4       R	R	R	4       R	#   + '       g   i     R	# ; i)
ry   )_count_paths_outside_method!_compute_outer_prob_inside_methodr  i  r   r~  re  iK  r9  N)scipy.stats._stats_pyr  r  r   r  r   FloatingPointError)rc   r  r  s   &  rm   test_some_code_paths%TestKSTwoSamples.test_some_code_paths  sq    	

 	*!Q15#D!Q5[[)),.Ia,,.Ia, *)))s   )A11B	r  c                H   \         P                  ! \        \        R 7      ;_uu_ 4        \        P
                  ! V!  p\        VP                  \        P                  4       \        VP                  \        P                  4       RRR4       R#   + '       g   i     R# ; ir  )r   rb  r   r   r[   r3  r   r>  r   rb   r=  rc   r  r   s   && rm   test_argument_checking'TestKSTwoSamples.test_argument_checking!  sY     \\,4IJJ..$'C/RVV, KJJJ   ABB!	c                4   \         P                  P                  R4       Rp\        P                  P                  VR^R7      pV^,           p\        P                  ! W#RRR7       \        P                  ! W#RRR7       \        P                  ! W#R	RR7       R
# )zEnsure gh-12218 is fixed.Na i    r   r%  r  r  r  r  r  N)r   r  r  r[   r  r  r3  )rc   r^  rvs1rvs2s   &   rm   test_gh12218TestKSTwoSamples.test_gh12218)  sm    
 			x }}  bb :axtywGtvGDt{Irp   c                   \         P                  P                  R R7      pVP                  RR7      R,           pVP                  RR7      pRp\        P                  ! \
        VR7      ;_uu_ 4        \        P                  ! W#RR	7      p\        VP                  ^ R
R7       RRR4       R#   + '       g   i     R# ; i)i{fr  iq  r  r1   iq  z(ks_2samp: Exact calculation unsuccessfulr   r  r  ri  rE  N)
r   r  r  r   rb  r   r[   r3  r
   r=  )rc   r  r  r  r  r   s   &     rm   test_warnings_gh_14019'TestKSTwoSamples.test_warnings_gh_140196  s     ii###2


$s*


$<\\.88..6BCCJJ6 9888s   21B--B>	r&  r'  c                   \         P                  ! ^
\         P                  R7      pVP                  4       pW6^&   \        P
                  ! WgVR7      pVP                  R8X  g   Q hVP                  V8X  g   Q hVP                  V8X  g   Q hR# )rO   r6   r  rD  N)	r   r   r   r@   r[   r3  r>  r)  r*  )	rc   r&  r  r+  r,  r-  rf   rg   r   s	   &&&&&&   rm   r.  #TestKSTwoSamples.test_location_signB  st     IIb

+FFH!nnQ{;}}###%%555!!X---rp   r   N)r  ))r  皙@r  rW   )r  ffffff@r   rU   )r  r  r  rW   )r  r  r   rU   )$r   r   r   r   r5  r  r6  r=  rA  rH  rN  rU  rX  r   r   r  ra  rf  rk  rr  rr  ru  r{  r~  r  r  r  r  r  r  r[   r  r3  r.  r   r   r   s   @rm   r1  r1  /  s    F>4
55	7:
L
= [[2 26 [[2 28	K$ [[$ $ [[	0 	0 [[( (.- [[, ,  [[VrA3i1#rRH%EF- G- [[
J 
J
7 [[Xenn'EF[[I;<

.< G
.rp   r1  c            
      n   R RrW ) .W.3p\         P                  ! ^^d^d4      p\         P                  ! RR^d4      p\         P                  ! \         P                  ! ^^d^d4      \         P                  ! RR^d4      .4      p\         P                  ! \         P                  ! RR^d4      \         P                  ! ^^d^d4      .4      p\        P                  ! W4^ R7      w  rx\        Wx.W34       \        P                  ! VP                  VP                  ^ R7      w  rx\        Wx.V4       \        P                  ! WV^R7      w  rx\        Wx.V4       \        4       ;_uu_ 4       p	\         P                  ! RRR7      ;_uu_ 4        V	P                  \        R4       \        P                  ! RR	4      w  rxR
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4       R
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4       \        \         P                  ! V4      4       \        \         P                  ! V4      4       R!p
\        P                  ! W4^ R7      p\        W4       \         P                  ! WUV.4      p\         P                  ! WfV.4      p\        P                  ! W^R7      w  rx\        \         P                  ! V4      V 4       \        \         P                  ! V4      V4       \!        VP"                  R"4       \        P                  ! \         P$                  ! V^^ 4      \         P$                  ! V^^ 4      ^R7      w  rx\        \         P                  ! V4      V 4       \        \         P                  ! V4      V4       \!        VP"                  R#4       \'        \(        \        P                  W4RR7       \        P                  ! W4^ RR7      w  rx\+        V^V^,          ,
          4       \+        Wp4       \        P                  ! W4^ RR7      w  rx\+        W^,          4       \+        Wp4       \         P,                  P/                  R4      p\        P0                  P3                  ^^
RVR7      p\         P4                  VR&   \        P0                  P3                  ^^
RVR7      \        P0                  P3                  RRVR7      ,           p\         P4                  VR&   \         P                  ! RR7      ;_uu_ 4        \7        \        P                  ! W4      \         P4                  \         P4                  34       R
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4       \8        P:                  ! \F        \H        R7      ;_uu_ 4        \        P                  ! WV^ RRR7      w  rxR
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#   + '       g   i     ELH; i  + '       g   i     ELT; i  + '       g   i     EL; i  + '       g   i     ELz; i  + '       g   i     ELp; i  + '       g   i     EL; i  + '       g   i     ELl; i  + '       g   i     EL6; i  + '       g   i     L; i  + '       g   i     R
# ; i)-gu?gȵI?r  gKX@r>   r}  r  r  r   r   Nr  r  r  r  r  r    r  r!  r4  )r$  r  r  r~  r   r   r   r   r  r   c                 l    V ^ 8  d   VR8X  g   V ^ 8  d   VR8X  d
   V^,          # ^V^,          ,
          # ry   r  r  r   r  re  alts   &&&rm   converttest_ttest_rel.<locals>.convert  3    EcVmQ3)3Cq5LAE{rp   re  ri  r  r  rW  r:  )ghm#1?gry̧?ry   ry   ry   r  rU   r;  )rF   r   rE   r   r   )r   :r  r  N)r   :r  r  N)%r   r5  r   r[   	ttest_relr   r   r   r  r   r   r   rw  r   r<  absr   r  r=  r   r   r
   r  r  rX  r  rb   r   r   rb  r!  rY  r   r]   	vectorizer   r   )trrH  tprr  r  rvs1_2Drvs2_2Dr  re  r   r@  r   rvs1_3Drvs2_3Dr  rf   rg   ananr  	converters                       rm   test_ttest_relr  U  su   !4rs8RG
C;;qS!D;;tF3'DhhAc#.D0LMNGhhD4bkk!C6LMNG
//$1
-CAqeRG,
//'))WYYQ
7CAqeC(
//'
3CAqeC( 
		KK::

>#FGr2& ; 
 BHHQKBHHQK )J
//$1
-C( ii12Gii12G
//'
3CAbffQi,bffQi,&!??2;;w15;;w15 !#DA bffQi,bffQi,&! *eootwO??4A6BDAAq2a4x A??4A9EDAA!tA ))


)C

1BSsCAVVAcF	ARc	D	c#	>
?AVVAcF	X	&	&5??102662662BC 
' eooavFGI*eooq!H*eooq!I 
n,E	F	Fy)4 
G"&&)Q"&&!-	X	&	&U__Y	:RVVRVV<LM xx!RVVr1g./U__T288F+;<"&&kArvv;/	1 
' 			"A*eooqyy/@))I&( W%IGHGH	(0A	B	B1H 
C 
(0A	B	Bw*0fF 
C A&	X	&	&9RV45A 
' 
(0A	B	Bw*0iI 
C A&	X	&	&9RY7eD 
'	&} ;:: 
		\ 
'	&	& 
G	F	F 
'	&	&. 
C	B	B 
C	B	B 
'	&	& 
C	B 
'	&	&s    !d0c0	1d?dd,Ce e(e(9e<?ff#0d;	dd	d)	,d=	 e	e%	(e9	<f	f 	#f4	c                     \         P                  R RR.p . R
Op\        P                  ! WRR7      p\        P                  ! WRR7      p\	        VP
                  VP
                  ) RR7       \	        VP                  VP                  RR7       \        P                  ! VR,          V R,          4      p\	        W4RR7       \	        VRRR7       R	# )r   r   r   r   r   rD  rE  r  -C6?Nr   r   r   r   )rZ  grh|?)r   rb   r[   r  r
   r>  r=  )rf   rg   r  r  r3s        rm   test_ttest_rel_nan_2nd_argr    s    	c3AA	&	1B	&	1BBLL2<<-e<BIIryyu5 
2"	&BB' B40rp   c                  h   \         P                  ! \        \        R 7      ;_uu_ 4        \        P
                  ! . . 4      p RRR4       \        X \        P                  P                  4      '       g   Q h\        V \        P                  \        P                  34       R#   + '       g   i     Lh; ir  )r   rb  r   r   r[   r  r7  	_stats_pyTtestResultr   r   rb   )r  s    rm   #test_ttest_rel_empty_1d_returns_nanr    sk     
(0E	F	FR( 
Gfeoo99::::"&&"&&)* 
G	Fs   B!!B1	b, expected_shapec                    \         P                  ! R4      p\         P                  P                  4       ;_uu_ 4       pVP	                  \
        \        4       \        P                  ! W RR7      pRRR4       \        X\        P                  P                  4      '       g   Q h\         P                  ! V\         P                  R7      p\        VP                  V4       \        VP                   V4       R#   + '       g   i     L; i)r   r>   Nr  r   rW   ry   rU   )r   rB  r"  r   r   r   r   r[   r  r7  r  r  r~   rb   r   r>  r=  )rW  expected_shaperK  r   r  expected_values   &&    rm   test_ttest_rel_axis_size_zeror    s     	A		%	%	'	'3

%'<=B/ 
( feoo99::::WW^?N!!>2/ 
(	's   3C88D	c                  f   \         P                  ! R4      p \         P                  ! R4      p\        P                  ! W^R7      p\	        V\        P
                  P                  4      '       g   Q h\        VP                  P                  R4       \        VP                  P                  R4       R# rW   r>   N)rW   rF   ry   rw   rF   rW   rw   ry   )r   rB  r[   r  r7  r  r  r   r>  r  r=  )rK  rW  r  s      rm    test_ttest_rel_nonaxis_size_zeror    sw    
 	A
A__Q*Ffeoo99::::!!''0$$f-rp   r  c                    \         P                  P                  R 4      p^
pVP                  VR^R7      pVP                  V^^R7      pRRR.RR\         P                  .R\         P                  ) R./p\
        P                  ! W4V R7      pVP                  R	R
7      p\        WuV ,          4       \        VP                  V^,
          4       R# )l   C67l:  r2   r%  r  gi{a?r  r  gC?r  r'  r(  NgZ?Yg8 )r   r  r  r  r!  r[   r  r  r
   r   r*  )r  r  r  rf   rg   r  r   r  s   &       rm   test_ttest_rel_ci_1dr    s     ))

 3
4C
A

s!
,A

q
*A +->?)2662RVVG013C //!K
8C		 	 $	 	7BBK()1rp   ztest_fun, argsc                     V ! V!  pR p\         P                  ! \        VR7      ;_uu_ 4        VP                  ^
R7       RRR4       R#   + '       g   i     R# ; i)r.  r   r(  N)r   r   r   r  )test_funr?  r   r  s   &&  rm   test_ttest_ci_ivr    sC    
 D/CDG	z	1	14 
2	1	1	1s   A

A	rd   c                `   a Sf   \        W4      MSoRV3R llpV! W4      V! W4      ,           # )Nc                    < SP                  V 4      p SP                  WR 7      pSP                  W^R7      pV P                  V,          pW#V3# )r>   r  )rY   r^   r   r  )rf   r?   mur   nobsrd   s   &&   rm   _stats_desc_stats.<locals>._stats-  sI    JJqMWWQW"ffQaf0wwt}}rp   r  )r&   )r  r  r?   rd   r  s   &&&d rm   _desc_statsr  *  s/    $&J	 BB "fR...rp   c                 b   V P                  R 4      pV P                  R4      pV P                  W) .4      pV P                  W".4      pV P                  ^^i^d4      pV P                  ^^d^d4      pV P                  WV.4      pV P                  We.4      p\        P                  ! WV^ R7      p	V	w  r\        W4       \        W4       \        P                  ! \        WV4      !  p	V	w  r\        W4       \        W4       \        P                  ! VP                  VP                  ^ R7      p	\        V	P                  V4       \        V	P                  V4       \        P                  ! \        VP                  VP                  4      !  p	\        V	P                  V4       \        V	P                  V4       \        P                  ! Wx^R7      p	\        V	P                  V4       \        V	P                  V4       \        P                  ! \        Wx^R7      !  p	\        V	P                  V4       \        V	P                  V4       Rp\        P                  ! \        VR7      ;_uu_ 4        \        P                  ! WVRR7       RRR4       \        VP                  VP                  4      p\        P                  ! \        VR7      ;_uu_ 4        \        P                  ! VRR/  RRR4       \        P                  ! WVR	R7      w  r\        V^V^,          ,
          4       \        W4       \        P                  ! WVR
R7      w  r\        W^,          4       \        W4       \        P                  ! VP                  VP                  ^ R	R7      p\        VP                  VP                  4      p\        P                  ! VRR	/ p\        VP                  VP                  4       \        VP                  VP                  4       \        P                  ! VP                  VP                  ^ R	R7      p\        VP                  VP                  4      p\        P                  ! VRR	/ p\        VP                  VP                  4       \        VP                  VP                  4       V P                  V P                  4      pV P                  V P!                  VP"                  ^ ,          4      ^ 8H  VV4      p\        P                  ! WV^ R7      p	\%        V	P                  V4       \%        V	P                  V4       \        P                  ! \        WV4      !  p	\%        V	P                  V4       \%        V	P                  V4       R#   + '       g   i     EL; i  + '       g   i     EL; i)	ru?g8Mѱ?r>   r  r   r  r  Nr  r  r  r  )rY   r  r5  r[   	ttest_indr/   ttest_ind_from_statsr  r   r>  r=  r   r   r   rb   rP  r   r  r0   )rd   r  rH  tr_2Dpr_2Dr  r  r  r  r   r  re  r  r?  r  r  NaNs   &                rm   test_ttest_indr  7  s    
&	'B	'	(BHHb#YEHHbXE;;q#s#D;;q#s#Dhh|$Ghh|$G
//$1
-CDAAA

$
$k$&=
>CDAAA
//'))WYYQ
7CCMM5)CJJ&

$
$k'))WYY&G
HCCMM5)CJJ&
//'
3CCMM5)CJJ&

$
$k'&K
LCCMM5)CJJ& IG	z	1	1': 
2 wyy')),D	z	1	1""D@@ 
2 ??46:DAAqBqDz"A??49=DAA!tA ??799giiaVLDwyy')),D%%t@@DDNNDNN3DKK-??799giiaVLDwyy')),D%%t@@DDNNDNN3DKK- **RVV
C88BIIdjjm,13=D
//$1
-CCMM3'CJJ$

$
$k$&=
>CCMM3'CJJ$M 
2	1	1 
2	1	1s   'V	V	V	V.	c            
         \         P                  ! ^^i^d4      p \         P                  ! ^^d^d4      p\         P                  ! W.4      p\         P                  ! W.4      p\         P                  ! W"V.4      p\         P                  ! W3V.4      p\         P                  P                  R4      p\        P                  P                  ^^
RVR7      p\         P                  VR&   \        P                  P                  ^^
RVR7      p\         P                  ! RR7      ;_uu_ 4        \        \        P                  ! Wx4      \         P                  \         P                  34       RRR4       \        \        P                  ! WxRR	7      R4       \        \        \        P                  WxR
R	7       \        \        \        P                  WxRR	7       \         P"                  ! \$        RR7      ;_uu_ 4        \        P                  ! . RO. RO4      w  rRRR4       \'        \         P(                  ! X	4      X
3\         P*                  ^ 34       \         P                  ! RR7      ;_uu_ 4        \'        \        P                  ! . RO. RO4      \         P                  \         P                  34       \         P                  ! ^\         P                  .R^..4      p\'        \        P                  ! V\         P,                  ! R4      4      ^ \         P                  .^\         P                  .34       RRR4       \         P                  VR&   \         P                  VR&   R p\         P.                  ! V4      p\        P                  ! WE^ RR7      w  r\        P                  ! WE^ RRR7      w  r\1        WRR7       \1        W! WR4      RR7       \        P                  ! WE^ RRR7      w  r\1        WRR7       \1        W! WR4      RR7       R#   + '       g   i     EL; i  + '       g   i     EL; i  + '       g   i     EL; i)rw   r  r  r  r!  r}  r~  Nr   r   r   r   r  r   c                 l    V ^ 8  d   VR8X  g   V ^ 8  d   VR8X  d
   V^,          # ^V^,          ,
          # r  r   r  s   &&&rm   r  *test_ttest_ind_nan_policy.<locals>.convert  r  rp   r  r  )r?   r   r  ri  r  r  )guͷ?g*,?r  r  rU   r;  )r   r   :rO   r  N)r   r   :rz   rQ   N)r   r5  r   r<  r  r  r[   rX  r  rb   r  r   r  r   r   r   r   rb  r   r   r  r!  rY  r  r
   )r  r  r  r  r  r  r  rf   rg   r  re  r  r  r  r  rH  s                   rm   test_ttest_ind_nan_policyr    s   ;;q#s#D;;q#s#Dhh|$Ghh|$Gii734Gii734G ))


)C

1BSsCAVVAcF

1BSsCA	X	&	&5??102662662BC 
' eooavFHJ*eooqH*eooqI 
n,E	F	Fy)4 
G"&&)Q"&&!-	X	&	&U__Y	:RVVRVV<LM xx!RVVr1g./U__T288F+;<"&&kArvv;/	1 
' 66GK&&GJ W%I__WA&IFB??7!'-/DAA&Ay0u=??7!'02DAA&Ay3%@S 
'	&	& 
G	F	F 
'	&	&s%   &?P5P#,CP7P 	#P4	7Q	c            	         \        4       ;_uu_ 4       p \        P                  ! R R7      ;_uu_ 4        V P                  \        R4       \
        P                  ! RR4      w  rRRR4       RRR4       \        P                  ! X4      '       g   Q h\        P                  ! X4      '       g   Q hR#   + '       g   i     LV; i  + '       g   i     La; i)r}  r~  r  r   r   N)r   r   r  r   r   r[   r  rw  )r   r  re  s      rm   test_ttest_ind_scalarr    s|    			R[[%B%B

>#FGr2& &C	 88A;;;88A;;;	 &C%B		s"    C0B1	#C1C<CC	z&ignore:Arguments...:DeprecationWarningc                     a  ] tR tRt o ^t]P                  P                  ^ 4       ]P                  ! ]P                  ! ^],          ^,          4      ]P                  P                  ^],          ^,          4      34      t
]P                  ! ]P                  ! ]^,          4      ^d,           ]P                  P                  ]^,          4      34      t]P                  ! ^
4      t]P                  ! ^
4      ^d,           t^^.t^^.t]P                  P                  ^ 4       ]P"                  P%                  ^^
RR7      P'                  ^d^4      P(                  t]P"                  P%                  ^^^dR7      tRR.tRR.t. ROt]
]R^/]3]
P(                  ]P(                  R^ /]3]
R ,          ]R ,          RR/]^ ,          3]
R ,          P5                  4       ]R ,          P5                  4       RR/]^ ,          3]
]R^ R^/]3]
]R]P                  P7                  ^ 4      R^/]3]]RR/R3]]RR!R^ /]3]]/ R"3]
]R]P                  P9                  ^ 4      R^/]3.
t]P>                  P@                  ]P>                  PC                  R	]4      R
 4       4       t"R t#R t$R t%R t&]P>                  PO                  4       R 4       t(R t)R t*R t+]P>                  PC                  R. R#O4      ]P>                  PC                  RR$R%.4      R 4       4       t,]P>                  PC                  R. R#O4      ]P>                  PC                  RR$R%.4      R 4       4       t-R t.]/! RRR7      R 4       t0Rt1V t2R# )&Test_ttest_ind_permutationsi  r!  r"  r?   Nr  	equal_varTza,b,update,p_dc                    R RRR/pR RRRRRR^ /pVP                  V4       VP                  V4       \        P                  ! W3/ VB w  rx\        P                  ! W3/ VB w  r\        Wy^4       \        W4       R# )r?   Nr  Fpermutationsr  r  )updater[   r  r   )rc   rK  rW  r  p_d	options_a	options_pstat_ar  stat_pr=  s   &&&&&      rm   test_ttest_ind_permutations7Test_ttest_ind_permutations.test_ttest_ind_permutations  s     T;6	T;#T>1>	  OOA6I6	;;!&!4!&.rp   c                b   \         P                  P                  ^ 4      p^pVP                  ^V^4      pVP                  ^V^4      pR^RR/pVP	                  RR7       \
        P                  ! W43/ VB p\
        P                  ! WC3/ VB pVP	                  RR7       \
        P                  ! W43/ VB p\
        P                  ! WC3/ VB p	VP	                  RR7       \
        P                  ! W43/ VB p
\
        P                  ! WC3/ VB p\        VP                  VP                  4       \        VP                  V
P                  4       \        VP                  VP                  ) 4       \        VP                  V	P                  ) 4       \        V
P                  VP                  ) 4       \        V
P                  VP                  4       \        VP                  V	P                  4       \        VP                  VP                  4       VP                  R8*  p\        VP                  V,          V	P                  V,          ,           V
P                  V,          4       \        VP                  V( ,          VP                  V( ,          ,           V
P                  V( ,          4       R	# )
ry   r?   r  r  r  r  r  r  r1   N
r   r  r  r  r  r[   r  r   r>  r=  )rc   r  NrK  rW  r  res_g_abres_g_bares_l_abres_l_bares_2_abres_2_bar  s   &            rm    test_ttest_ind_exact_alternative<Test_ttest_ind_permutations.test_ttest_ind_exact_alternative  s   ii##A&HHQ1HHQ1Q5	Y/??1595??1595V,??1595??1595[1??1595??1595 	X''););<X''););< 	X''(*<*<)<=X''(*<*<)<=X''(*<*<)<= 	X__hoo6 	X__hoo6X__hoo6#%X__T*X__T-BB__T*	,X__dU+hoote.DD__dU+	-rp   c                   \         P                  P                  ^ 4      p^pVP                  V4      pVP                  V4      p\        P
                  ! W44      p\        P
                  ! W4RR7      p\        P
                  ! W4^ R7      p\        P
                  ! W4\         P                  R7      pVP                  VP                  8w  g   Q hVP                  VP                  8X  g   Q hVP                  VP                  8X  g   Q hR# )ry   r  r  N)r   r  r  r  r[   r  r!  r=  )	rc   r  r  rK  rW  r  r  r  r  s	   &        rm   test_ttest_ind_exact_selection:Test_ttest_ind_permutations.test_ttest_ind_exact_selection1  s    ii##A&HHQKHHQKq$q$7q!4q"&&9{{dkk))){{dkk))){{dkk)))rp   c                   \         P                  P                  ^ 4      pVP                  ^4      pVP                  ^4      p\         P                  ! W#34      p\        V4      \        V4      reRp\        WGVR4      w  p p	\        \        V4      4      p
V
\        WV,           V4      8X  g   Q h\        V4      V
8X  g   Q hR# )ry   r^  TN)	r   r  r  r  rz  r   r   ra   r   )rc   r  rK  rW  r  nanbr  t_statr  n_uniques   &          rm   !test_ttest_ind_exact_distribution=Test_ttest_ind_permutations.test_ttest_ind_exact_distribution?  s     ii##A&HHQKHHQK~~qf%QQB24r3791 s6{#5"----6{h&&&rp   c                r   \         P                  P                  ^ 4      p^2pVP                  ^^V4      pVP                  ^V4      pRR	RRR^ /pVP	                  RR7       \
        P                  ! W43/ VB p\
        P                  ! WC3/ VB pVP	                  RR7       \
        P                  ! W43/ VB p\
        P                  ! WC3/ VB p	\        VP                  VP                  4       \        VP                  VP                  ) 4       \        VP                  V	P                  ) 4       \        VP                  VP                  ,           ^^VR,          ^,           ,          ,           4       \        VP                  V	P                  ,           ^^VR,          ^,           ,          ,           4       R# )
ry   r?   r  r  r  r  r  r  NrU   r  )
rc   r  r  rK  rW  r  r  r  r  r  s
   &         rm   #test_ttest_ind_randperm_alternative?Test_ttest_ind_permutations.test_ttest_ind_randperm_alternativeR  sf   ii##A&HHQ1HHQNR~qI	Y/??1595??1595V,??1595??1595 	X''););< 	X''(*<*<)<=X''(*<*<)<= 	X__x6In59::	<X__x6In59::	<rp   c                   \         P                  P                  ^ 4      p^2pVP                  V^4      pVP                  V^4      pRRR^ /pVP	                  RR7       \
        P                  ! W43/ VB pVP	                  RR7       \
        P                  ! W43/ VB pVP	                  RR7       \
        P                  ! W43/ VB p\        VP                  VP                  ,           ^^VR,          ^,           ,          ,           4       VP                  R8*  p	\        ^VP                  V	,          ,          VP                  V	,          R	R
7       \        ^^VP                  V	( ,          ,
          ,          VP                  V	( ,          R	R
7       \        ^VP                  V	( ,          ,          VP                  V	( ,          R	R
7       \        ^^VP                  V	,          ,
          ,          VP                  V	,          R	R
7       R# )ry   r  r  r  r  r  r  r  r1   rD  rE  N)
r   r  r  r  r  r[   r  r   r=  r
   )
rc   r  r  rK  rW  r  r  r  r  r  s
   &         rm   $test_ttest_ind_randperm_alternative2@Test_ttest_ind_permutations.test_ttest_ind_randperm_alternative2o  s   ii##A&HHQNHHQN#UNA>	Y/??1595V,??1595[1??1595 	X__x6In59::	<
 #%HOOD11 -D	:Qxu556 .T	;HOOTE22 .T	;Qxt445 -D	:rp   c                   \         P                  P                  ^ 4      p^2pVP                  V^4      pVP                  V^4      p\         P                  VR&   \         P                  VR&   \         P                  VR&   \         P                  VR&   RRR^ /pVP                  RR7       \        \        RR7      ;_uu_ 4        \        P                  ! W43/ VB pRRR4       \        4       ;_uu_ 4       pVP                  \        R	4       VP                  R
R7       \        P                  ! W43/ VB p\         P                  ! V4      P                  ^ R7      \         P                  ! V4      P                  ^ R7      ,          p\        P                  ! VRV( 3,          VRV( 3,          3/ VB p	\        VP                   V,          \         P                  4       \        VP"                  V,          \         P                  4       \%        VP                   V( ,          V	P                   4       \%        VP"                  V( ,          V	P"                  4       \        P                  ! VP'                  4       VP'                  4       3/ VB p\         P                  ! VP                   4      '       g   Q h\         P                  ! VP"                  4      '       g   Q h RRR4       R#   + '       g   i     EL; i  + '       g   i     R# ; i)ry   r  r  r  r   r   r   r   Nr   r  r>   r   rw   rW   )rF   rE   )rI   r   )r   r  r  r  rb   r  r   r   r[   r  r   r   r   rw  r  r   r=  r>  r
   r  )
rc   r  r  rK  rW  r  r   r   r  r  s
   &         rm   $test_ttest_ind_permutation_nanpolicy@Test_ttest_ind_permutations.test_ttest_ind_permutation_nanpolicy  s$   ii##A&HHQNHHQN&&$&&$&&$&&$#T>1=	 	G,:-LMM//!4)4C N   CJJ~'784//!4)4C88A;???*RXXa[__!_-DDD??1QX;!dU(IyIDD)2662t,bff5CJJu-t{{;CMM4%0$..A //!'')QWWYD)DC88CJJ''''88CMM****# ! 	 NMM !  s   K'5G$K;K;'K8	;L	c           
     X   \        \        R R7      ;_uu_ 4        \        P                  ! V P                  V P
                  RR7       RRR4       \        \        R R7      ;_uu_ 4        \        P                  ! V P                  V P
                  RR7       RRR4       \        \        RR7      ;_uu_ 4        \        P                  ! V P                  V P                  ^R^R7       RRR4       R#   + '       g   i     L; i  + '       g   i     Lv; i  + '       g   i     R# ; i)	zPermutations must ber   r  Nr2   z'hello' cannot be usedhello)r  r  r?   rV   )r   r   r[   r  r  b2rK  rW  r|  s   &rm   'test_ttest_ind_permutation_check_inputsCTest_ttest_ind_permutations.test_ttest_ind_permutation_check_inputs  s    :-CDDOODGGTWW2> E:-CDDOODGGTWW3? E:-EFFOODFFDFF)0q: GF	 EDDDFFFs#   .C2).D80D2D	D	D)	c                    ^
p\         P                  P                  V^4      p\         P                  P                  V^4      p\        P                  ! W#^R7      P
                  p\        RV9  4       RV9  g   Q hR# )rO   r  r   N)r   r  r  r[   r  r=  print)rc   r  rK  rW  p_valuess   &    rm   )test_ttest_ind_permutation_check_p_valuesETest_ttest_ind_permutations.test_ttest_ind_permutation_check_p_values  s`    IINN1b!IINN1b!??1a8??c!"("""rp   r  r  c           	        \         P                  P                  R 4      pVP                  VR7      pVP                  ^R7      p\        RR7      p\         P                  P                  R4      p\        P
                  ! RRV/VB p\        P                  ! WERWR7      pR p	\         P                  P                  R4      p\        P                  ! WE3V	3RRRVR	V/VB p
\        VP                  V
P                  4       \        VP                  V
P                  4       \        P                  ! WERVR
7      p
\        VP                  V
P                  4       \        VP                  V
P                  RR7       R# )   Nvf_aB r    re     N\Sju	 r  r?   r  r  c                 F    \         P                  ! WVR 7      P                  # r>   r[   r  r>  rf   rg   r?   s   &&&rm   r>  FTest_ttest_ind_permutations.test_permutation_method.<locals>.statistic      %//!T*J*T*T#Trp   r?   r  r  r  r  Nr   rU   )r   r  r  r  r[   r  r  permutation_testr   r>  r=  r
   )rc   r  r  r  rf   rg   r@  r  r   r>  r  s   &&&        rm   test_permutation_method3Test_ttest_ind_permutations.test_permutation_method  s6    ii##$45JJEJ"JJBJ#& ii##O4((;S;F;ooaT 	Uyy$$_5$$aVY HR HS H1<H@FH 	S]]CMM2SZZ, ooaES]]CMM2

CJJT:rp   c                @   \         P                  P                  R 4      pVP                  VR7      pVP                  ^R7      p\        RR7      pR p\         P                  P                  R4      pVP                  VP                  .p\
        P                  ! WE33RVRVRRR	V/VB p	\         P                  P                  R4      pVP                  VP                  .p\
        P                  ! RRV/VB p
\
        P                  ! WERWR
7      p\        VP                  V	P                  4       \        VP                  V	P                  4       \
        P                  ! RRR/VB p
\
        P                  ! WERWR
7      p\        VP                  V	P                  4       \        VP                  V	P                  4       \
        P                  ! WERVR7      p	\        VP                  V	P                  4       \        VP                  V	P                  RR7       R# )r	  r  r	  r	  c                 F    \         P                  ! WVR 7      P                  # r"	  r#	  r$	  s   &&&rm   r>  FTest_ttest_ind_permutations.test_monte_carlo_method.<locals>.statistic  r&	  rp   r	  r  r>  r?   r  r 	  r  r  r  r  NrU   r   )r   r  r  r  r  r[   monte_carlo_testr  r  r   r>  r=  r
   )rc   r  r  r  rf   rg   r@  r>  r  r  r  r   s   &&&         rm   test_monte_carlo_method3Test_ttest_ind_permutations.test_monte_carlo_method  s    ii##$45JJEJ"JJBJ#& 	Uii##O4""C$7$78$$aV H H	 HPR H1<H@FH ii##O4""C$7$78'':C:6:ooaTS]]CMM2SZZ, ''FOFvFooaTS]]CMM2SZZ, ooaES]]CMM2

CJJT:rp   c                    R p\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! . RO. RORR7       RRR4       R#   + '       g   i     R# ; i)zC`method` must be an instance of `PermutationMethod`, an instance...r   	migratoryr  Nr  r+  )r   r   r   r[   r  r;  s   & rm    test_resampling_input_validation<Test_ttest_ind_permutations.test_resampling_input_validation  s7    W]]:W55OOIyE 6555s   AA 	Uses NumPy for pvalue, CIcpu_onlyr   c                   VP                  V P                  4      VP                  V P                  4      r2R p\        V4      '       d   \        P
                  ! W#^
R7       ME\        P                  ! \        VR7      ;_uu_ 4        \        P
                  ! W#^
R7       RRR4       Rp\        P                  P                  R4      p\        P                  ! VR7      p\        V4      '       d   \        P
                  ! W#VR7       R# \        P                  ! \        VR7      ;_uu_ 4        \        P
                  ! W#VR7       RRR4       R#   + '       g   i     L; i  + '       g   i     R# ; i)z;Use of `permutations` is compatible only with NumPy arrays.r  r   Nz?Use of resampling methods is compatible only with NumPy arrays.l   /gGy r  r  )rY   r  r	  r)   r[   r  r   r   r  r   r  r  r  )rc   rd   r  r	  r  r  r  s   &&     rm   %test_permutation_not_implement_for_xpATest_ttest_ind_permutations.test_permutation_not_implement_for_xp  s    DGG$bjj&9BOB<<OOB42'BBR8 C Tii##$45((S1B<<OOB622'BBv6 CB CB CBBs   E.E$E!	$E5	r   g'^P?gCq?g$R?)g=B?g?goŜ?gp?g'^?rq  rU   rV  r
  )rQ   )rE   rQ   )3r   r   r   r   r  r   r  r  r  r   rK  rW  r  r	  r  b3r[   rX  r  r]   r   r  r  r  p_d_genp_d_bigr{   r  r  paramsr   r   thread_unsafer  r  r  r  r	  r	  r  r	  r	  r	  r	  r(	  r.	  r2	  r   r8	  r   r   r   s   @rm   r  r    sk    
A IINN1
		299QqS!V$bii&6&6qsAv&>?@A
		299QT?S("))*:*:1a4*@ABA 
2B	2	B QB
QB IINN1::>>ar"  $$+GCOAA 	::>>ar>4D<
 C~&G+G 
A{C 	
accFA;$	
4!D'FD>3q62	
4	1T7>>+fd^SVD	
A61-s3	
A		 5 5a 8&!DcJ	R+t$f-	tfb.!4g>	RS	
A		 5 5a 8&!DgN
F [[[[-v6
/ 7 
/(-T*'&<: [[: :B"+H:# [[],LM[[Wug&67; 8 N;4 [[],LM[[Wug&67; 8 N;BF
 t,GH7 I7rp   r  c                     a  ] tR tRt o ]P
                  P                  4       ]P
                  P                  RR^R^ /RR// .. ROR7      ]P
                  P                  RR	R
.RR.R7      R 4       4       4       t]P
                  P                  RR^R^ /RR// .. ROR7      ]P
                  P                  RR^ .4      R 4       4       t	Rt
V tR# )Test_ttest_ind_commoni   kwdsr  r  trimr4  )idsr  TFunequal_varc                f   \         P                  P                  ^ 4       \         P                  P                  ^^^^^^4      p\         P                  P                  ^^^^^4      p\        P
                  ! W43RR/VB p^^^rpW6RVR^ R3,          p	VR^ RVR3,          p
\        P
                  ! W3RR/VB p\        VP                  VRWxR3,          VP                  4       \        VP                  VRWxR3,          VP                  4       \         P                  ! \         P                  ! VR4      RR4      p\         P                  ! \         P                  ! VR	4      RR4      pVP                  RR p\         P                  ! V4      p\         P                  ! V4      p\        R V 4       !   FM  pVV,          pVV,          p\        P
                  ! VV3RR/VB pVP                  VV&   VP                  VV&   KO  	  \        WP                  4       \        VVP                  4       R# )
ry   r?   r   Nc              3   8   "   T F  p\        V4      x  K  	  R # 5ir  r  .0r  s   & rm   	<genexpr>=Test_ttest_ind_common.test_ttest_many_dims.<locals>.<genexpr>C  s      95aq5   rV   rZ  rW   rW   rW   rW   rE   rW   rU   rw   rW   r   rW   rW   rW   )r   r  r  r  r[   r  r   r>  r=  r=  tiler  rY  r   r
   )rc   rA	  r  rK  rW  r   r  r  r  r  r	  r  rf   rg   r  
statisticspvaluesindicesxiyir  s   &&&                  rm   test_ttest_many_dims*Test_ttest_ind_common.test_ttest_many_dims$  s    			qIINN1aAq!,IINN1aAq)ooa44t4 Qa!Q1a q!Q1}r7B7$7S]]1aq=1^^	%SZZ1aA.[[	" KK#56B?KK#56B?XXe_
((5/ 95 9:G7B7B??2r;;d;D"&..Jw#{{GG ; 	
MM2,rp   r?   c           	        \         P                  P                  R 4      pVP                  ^
R
R7      P	                  R4      pVP                  ^
R
R7      P	                  R4      p\         P
                  V^ ,          ^,          ^&   \         P
                  V^,          ^ ,          ^&   \         P                  ! \         P                  ! WE,           VR7      4      p\        4       ;_uu_ 4       p\         P                  ! RR7      ;_uu_ 4        VP                  \        R4       VP                  \        R4       \        P                  ! WE3RV/VB pR	R	R	4       R	R	R	4       \         P                  ! XP                  4      p	\        W4       \         P                  ! VP                   4      p
\        W4       R	#   + '       g   i     Lp; i  + '       g   i     L{; i)l   AoI;r  r  r>   r}  r~  z'invalid value encountered in less_equalr  r?   N)rw   r   rO   )r   r  r  integersr  rb   rw  r^  r   r  r   r   r[   r  r=  r   r>  )rc   rA	  r?   r  rK  rW  r  r   r   p_nansstatistic_nanss   &&&        rm   test_nans_on_axis'Test_ttest_ind_common.test_nans_on_axisM  s>    ii##$9:LL*L-44W=LL*L-44W=VV!Q
VV!Q
 88BFF15t45   CX)F)FJJ~@BJJ~'@A//!:T:T:C	 *G 
 #**%6,#--0>4 *G)F  s%   * G
AF8	G8GGG	r   N)r  rB	  basic)rB	  r  r]	  rU   )r   r   r   r   r   r   rr  r  rU	  r[	  r   r   r   s   @rm   r@	  r@	     s      [[[[V~sNA&N'-rlB&8!B  D [[[4-"-}!=  ?!-?D !-F [[V~sNA&N'-rlB&8!B  D [[Vb!W-5 .D5rp   r@	  c            	         a  ] tR tRt o . RO. RORRR.. RO. RORRR.. RO. RORRR.. RO. ROR	R R.. R!O. R"OR
R#R..t]P                  P                  R]4      R 4       tR t	R t
]P                  P                  RR$4      R 4       tR t]! RRR7      R 4       t]P                  P                  R. R%O4      R 4       tRtV tR# )&Test_ttest_trimik  g9(?r4  gBM)u?g]@gyd?g	s5v@g{Gz?gn4aƂg?g!nu?za,b,pr,tr,trimc                p    \         P                  ! WVRR7      w  rg\        WdRR7       \        WsRR7       R# )a8  
Using PairedData's yuen.t.test method. Something to note is that there
are at least 3 R packages that come with a trimmed t-test method, and
comparisons were made between them. It was found that PairedData's
method's results match this method, SAS, and one of the other R
methods. A notable discrepancy was the DescTools implementation of the
function, which only sometimes agreed with SAS, WRS2, PairedData and
this implementation. For this reason, most comparisons in R are made
against PairedData's method.

Rather than providing the input and output for all evaluations, here is
a representative example:
> library(PairedData)
> a <- c(1, 2, 3)
> b <- c(1.1, 2.9, 4.2)
> options(digits=16)
> yuen.t.test(a, b, tr=.2)

    Two-sample Yuen test, trim=0.2

data:  x and y
t = -0.68649512735573, df = 3.4104431643464, p-value = 0.5361949075313
alternative hypothesis: true difference in trimmed means is not equal
to 0
95 percent confidence interval:
 -3.912777195645217  2.446110528978550
sample estimates:
trimmed mean of x trimmed mean of y
2.000000000000000 2.73333333333333
FrB	  r  rD  rE  Nr[   r  r
   )rc   rK  rW  rH  r  rB	  r>  r=  s   &&&&&&  rm   test_ttest_compare_r$Test_ttest_trim.test_ttest_compare_r  s.    @ "OOAtuM		E2/rp   c                    . R	Op. R
Op\         P                  ! WRRR7      w  r4\        VRRR7       \        VRRR7       R# )rQ   g
ףp=
?Fra	  gRbv?r  rE  gOi?N)rQ   rM   r  r  r  ,   rQ   rM   r  r  r  rf	  )      rM   rQ   r     r  rg	  rh	  rM   rQ   r  ri	  r  rb	  rc   rK  rW  r>  r=  s   &    rm   test_compare_SAS Test_ttest_trim.test_compare_SAS  s=     =D "OOAseL	t4	8$7rp   c                    . ROp. ROp\         P                  ! WRR7      w  r4\        VRRR7       \        VR	RR7       R# )
a^  
The PairedData library only supports unequal variances. To compare
samples with equal variances, the multicon library is used.
> library(multicon)
> a <- c(2.7, 2.7, 1.1, 3.0, 1.9, 3.0, 3.8, 3.8, 0.3, 1.9, 1.9)
> b <- c(6.5, 5.4, 8.1, 3.5, 0.5, 3.8, 6.8, 4.9, 9.5, 6.2, 4.1)
> dv = c(a,b)
> iv = c(rep('a', length(a)), rep('b', length(b)))
> yuenContrast(dv~ iv, EQVAR = TRUE)
$Ms
   N                 M wgt
a 11 2.442857142857143   1
b 11 5.385714285714286  -1

$test
                      stat df              crit                   p
results -4.246116897032513 12 2.178812829667228 0.00113508833897713
r4  rB	  gR?r  rE  Nr  r  r  r   ffffff?r   r  r  rG  rp	  rp	  rC   g@r  r  r1   r  g333333@r  r  g@r  g^rb	  rj	  s   &    rm   test_equal_varTest_ttest_trim.test_equal_var  s<    & DC!OOAr:	 3%@	#5EBrp   z	alt,pr,trc                    . ROp. ROp\         P                  ! WERRVR7      w  rg\        WrRR7       \        WcRR7       R# )	z
> library(PairedData)
> a <- c(2.7,2.7,1.1,3.0,1.9,3.0,3.8,3.8,0.3,1.9,1.9)
> b <- c(6.5,5.4,8.1,3.5,0.5,3.8,6.8,4.9,9.5,6.2,4.1)
> options(digits=16)
> yuen.t.test(a, b, alternative = 'greater')
r4  F)rB	  r  r  r  rE  Nro	  rq	  rb	  )rc   r  rH  r  rK  rW  r>  r=  s   &&&&    rm   test_alternatives!Test_ttest_trim.test_alternatives  s=     DC!OOArU8;=	/	E2rp   c                b   R p\        \        VR7      ;_uu_ 4        Rp\        P                  ! \        VR7      ;_uu_ 4        \
        P                  ! ^^.^^.R^R7       RRR4       RRR4       \        \        VR7      ;_uu_ 4        Rp\        P                  ! \        VR7      ;_uu_ 4        \
        P                  ! ^^.^^.R^^R7       RRR4       RRR4       R#   + '       g   i     L; i  + '       g   i     L; i  + '       g   i     L@; i  + '       g   i     R# ; i)z>Use of `permutations` is incompatible with with use of `trim`.r   z5Arguments {'permutations'} are deprecated, whether...r4  )rB	  r  Nz9Arguments {.*'random_state'.*} are deprecated, whether...)rB	  r  r  )r   r  r   rb  DeprecationWarningr[   r  )rc   r   r  s   &  rm   test_errors_unsupported'Test_ttest_trim.test_errors_unsupported  s    P.e<<MG0@@AARaH A =
 .e<<QG0@@AARa-.0 A =< A@ =< A@ =<<sG   'C7C$	"C7'D2 D
	D$C4/C77D	
DDD.	Tr4	  r5	  c                b   R pVP                  ^
4      VP                  ^
4      ^,           rC\        V4      '       d   \        P                  ! W4RR7       R# \        P
                  ! \        VR7      ;_uu_ 4        \        P                  ! W4RR7       RRR4       R#   + '       g   i     R# ; i)z3Use of `trim` is compatible only with NumPy arrays.rD  rn	  r   N)r   r)   r[   r  r   r   r  )rc   rd   r  rK  rW  s   &&   rm   r8	  5Test_ttest_trim.test_permutation_not_implement_for_xp  si    Gyy}biimAo1B<<OOAs+2'BB3/ CBBBs   :BB.	rB	  c                    R p\        \        VR7      ;_uu_ 4        \        P                  ! ^^.^^.VR7       RRR4       R#   + '       g   i     R# ; i)z/Trimming percentage should be 0 <= `trim` < .5.r   rn	  N)r   r   r[   r  )rc   rB	  r   s   && rm   test_trim_bounds_error&Test_ttest_trim.test_trim_bounds_error  s;    A:U33OOQFQF6 4333s   AA	r   Nr  r  r  g@ge)rK  g33333`@rQ   g33333^@g(\P@r  gfffffڇ@ro	  rq	  ^)g,
gm?giI@gE|x!gvwQ?glfPg_)gXG~?g=n@g8$mg({g]:m?gYv gb?gb	gSTß}g9yg.Ͽv?g޺i?g	'X@)g>_\?g hO?gau?@g׌g+?g:؜^gz54g7f?gDO%@g#xG@g\F?g4E?gnfg>P"ۿguX@gvR?g%?g2Ydzgo?gih?gn?gJ+b))r  gjΜ>5?r	  )r  gn4aƂW?r	  )gɿr1   rW   )r   r   r   r   r=	  r   r   r  rc	  rk	  rr	  ru	  ry	  r   r8	  r~	  r   r   r   s   @rm   r_	  r_	  k  s    	O%8:M			1?	/	5	1?	/	6	@	@	,b	2
H
  "34Db	JKF& [[-v6!0 7!0F8C4 [[[N3	3 0 t,GH0 I0 [[V\27 37rp   r_	  c                   T  a  ] tR tRt o ]P
                  ! RR7      t. RO]R &   RRR]P                  ) R.]R!&   RRRR"]P                  .]R#&   . R%O]R&&   R$RR]P                  ) R	.]R'&   R$RR
R(]P                  .]R)&   R*^R]P                  ]P                  .]R+&   R*^R]P                  ]P                  .]R,&   R*^R]P                  ]P                  .]R-&   R.^R]P                  ]P                  .]R/&   R.^R]P                  ]P                  .]R0&   R.^R]P                  ]P                  .]R1&   ]	P                  P                  R. R2O4      ]	P                  P                  RRR.4      ]	P                  P                  R^ R.4      ]! RRR7      R 4       4       4       4       tRtV tR# )3Test_ttest_CIi  )r  e13@gv7?gx_?g
/?-</&@g?JJ?gF?g{?gW"?gW"?g:T'?g0:5?g0:5?g be?r  r  FTrB	  r4  r"  r#  r  c                    V'       d   V'       d   \         P                  ! R 4       V'       d(   \        V4      '       g   \         P                  ! R4       \        P
                  P                  R4      pVP                  VP                  ^4      4      pVP                  VP                  ^4      4      p\        P                  ! WgVW#R7      pR^ R^R^/p	V P                  W,          \        V4      \        \        P                  ! V4      4      3,          p
V
w  rrpRp\        VP                  VP                  V4      VR7       \        VP                  VP                  V4      VR7       \        VP                   VP                  V4      VR7       V'       gb   VP#                  R	4      p\        VP$                  VP                  V4      VR7       \        VP&                  VP                  V4      VR7       R
# R
# )z3Discrepancy in `main`; needs further investigation.z*`trim` is only compatible with NumPy inputl   'Nk' )r  r  rB	  r  r  r  r  r  rF  N)r   xfailr)   r  r   r  r  rY   r[   r  r   r!  ceilr/   r>  r*  r=  r  r  r  )rc   r  r  rB	  rd   r  rf   rg   r   r  r  r>  r*  r=  r  r  r  r  s   &&&&&             rm   test_confidence_interval&Test_ttest_CI.test_confidence_interval+  se   
 LLNOKKDEii##$78JJszz"~&JJszz"~&ooa(1> $Q9a@ff\.IBGGDM@RRS+.(	vDrzz)'<4H

2T:

BJJv$6TB((-BBFFBJJsO$?BGGRZZ%5DA rp   r   N)r   rE   rE   rw   gͿ)r	  r	  gv7?gę"Ͽg8 {M(?r  rW   ry   ry   gD .ɿ)rE   ry   ry   reϿ)r	  r	  g?JJ?gbտg3Պ?)ry   ry   rW   )rW   ry   rW   gads2ѿ)rE   ry   rW   gs"%ο)ry   rW   ry   rW   rW   ry   )rE   rW   ry   g:пr  r  )rE   rW   rW   rn  )r   r   r   r   r   rB  r   r!  rb   r   r   r  r   r	  r   r   r   s   @rm   r	  r	    s    < 	|$ANAgJibffWlKAgJiM266JAgJLAgJibffWlKAgJiL"&&IAgJ%r+=rvvrvvNAgJ%r+=rvvrvvNAgJ%r+=rvvrvvNAgJ%r+=rvvrvvNAgJ%r+=rvvrvvNAgJ%r+=rvvrvvNAgJ[[],LM[[[5$-8[[VaX.k*JKB L / 9 NBrp   r	  c            	      z   \         P                  P                  ^ 4       \         P                  P                  ^^^^^^4      p \         P                  P                  ^^^^^4      p\	        W3RR7      p\         P
                  ! V R4      p \         P
                  ! VR,          R4      p\        R VP                   4       !   Fs  pVw  rErgrWpP                  R,          8  d    WWVWxV	3,          W$WVWxV	3,          8X  g   Q hK?  WWVWpP                  R,          ,
          W3,          W$WVWxV	3,          8X  d   Ks  Q h	  R# )ry   r>   Nc              3   8   "   T F  p\        V4      x  K  	  R # 5ir  rG	  rH	  s   & rm   rJ	  .test__broadcast_concatenate.<locals>.<genexpr>V  s     5W588WrL	  rV   rM	  )N.rN	  )r   r  r  r  r   rO	  r   r  )
rK  rW  rj  indexr  r  r  r5  r  r  s
             rm   test__broadcast_concatenater	  L  s    IINN1
		q!Q1a(A
		q!Q1%AvB/A
%&A
)01A5QWW56 aAwwr{?aA%&!qQ1,<*====a''"+oq34Q1:J8KKKK 7rp   c                   v  a  ] tR tRt o ]! ]P                  4      R 4       t]P                  P                  R4      ]P                  P                  R4      R 4       4       tR tR t]P                  P                  R]P                   ! R4      R3]P                   ! R4      R3.4      R	 4       tR
 tR tRtV tR# )TestTTestIndi^  c                l   VP                  . RO4      pVP                  . RO4      pVP                  R4      pVP                  R4      p\        P                  ! W#RR7      w  rg\        We4       \        Wt4       \        P                  ! \        W#4      RR/ w  rg\        We4       \        Wt4       VP                  . RO4      pVP                  R4      pVP                  R4      p\        P                  ! W#RR7      w  rg\        We4       \        Wt4       \        P                  ! \        W#4      RR/ w  rg\        We4       \        Wt4       VP                  R4      pVP                  R4      pVP                  R4      pVP                  R	4      p	VP                  WU) .4      p
VP                  WD.4      pVP                  ^^d^4      pVP                  ^^d^d4      pVP                  ^^i^d4      pVP                  W.4      pVP                  W.4      p\        P                  ! W^ RR
7      w  rg\        We4       \        Wt4       \        P                  ! \        W4      RR/ w  rg\        We4       \        Wt4       \        P                  ! W^ RR
7      w  rg\        Wh4       \        Wy4       \        P                  ! \        W4      RR/ w  rg\        Wh4       \        Wy4       \        P                  ! VP                  VP                  ^ RR
7      p\        VP                  V
4       \        VP                  V4       \        VP                  VP                  4      p\        P                  ! VRR/ p\        VP                  V
4       \        VP                  V4       \        P                  ! VV^RR
7      p\        VP                  V
4       \        VP                  V4       \        VV^R7      p\        P                  ! VRR/ p\        VP                  V
4       \        VP                  V4       R# )r   g9(?Fr  r  gJ?r  g@[?gωұ?ghG?)r?   r  r>   Nr  r	  gerD  g9ʿ)rY   r[   r  r/   r  r  r  r5  r   r>  r=  )rc   rd   rK  rW  rH  r  r  re  	tr_uneq_n	pr_uneq_nr  r  rvs3r  r  r  r  r   r?  s   &&                 rm   test_ttest_ind_with_uneq_var)TestTTestInd.test_ttest_ind_with_uneq_var`  sI    JJ|$JJ'ZZ+,ZZ-.qu5));q+<NNJJ'(ZZ+,ZZ-.qu5));q+<NN ZZ*+JJ23	ZZ+,JJ23	"c#""{{1c2&{{1c3'{{1c3'((D<(((D<(tUC));t+BTeTtUC%%));t+BTeT%%oogiieLu-

E*799gii0(($@%@u-

E*oogwQ%Hu-

E*7G!4(($@%@u-

E*rp   0ignore:divide by zero encountered:RuntimeWarning/ignore:invalid value encountered:RuntimeWarningc           	        VP                  ^4      pVP                  ^4      p\        V\        RR7      ;_uu_ 4        \        P
                  ! W#RR7      w  rERRR4       \        XVP                  VP                  ) 4      4       \        XVP                  R4      4       \        P                  ! RR7      ;_uu_ 4        \        P
                  ! W"RR7      w  rE\        WAP                  VP                  4      4       \        WQP                  VP                  4      4       VP                  ^VP                  .R
^..4      p\        P
                  ! WaP                  R4      RR7      w  rE\        WAP                  R\        P                  .4      4       \        WQP                  R	\        P                  .4      4       RRR4       R#   + '       g   i     EL|; i  + '       g   i     R# ; i)r   r  r   Fr	  Nr   r}  r  r   rU   r;  )rY  r  r'   r   r[   r  r0   rY   r!  r   r  rb   )rc   rd   rf   rg   r  re  r  s   &&     rm   test_ttest_ind_zero_division)TestTTestInd.test_ttest_ind_zero_division  sM    HHQKGGAJN2KLL??159DA M 	2::rvvg./2::b>*[[X&&??159DAAzz"&&12Azz"&&12 ::266{RG45D??4&)9UKDAAzz2rvv,78Azz2rvv,78 '& MLL '&&s   G DGG	G0	c                   \         P                  R RR.p. R	Op\        P                  ! WRR7      p\        P                  ! W!RR7      p\	        VP
                  VP
                  ) RR7       \	        VP                  VP                  RR7       \        P                  ! W!R,          4      p\	        WERR7       \	        VR
RR7       R# )r   r   r   r   r   rD  rE  r  Nr  )g8HgW@?)r   rb   r[   r  r
   r>  r=  )rc   rf   rg   r  r  r  s   &     rm   test_ttest_ind_nan_2nd_arg'TestTTestInd.test_ttest_ind_nan_2nd_arg  s    VVS#s# __Qf5__Qf5r||m%@		29959 __Q"&U+ 	G"	$rp   c                z   \        V4      '       dh   \        P                  ! \        \        R 7      ;_uu_ 4        \
        P                  ! VP                  . 4      VP                  . 4      4      pRRR4       M5\
        P                  ! VP                  . 4      VP                  . 4      4      p\        X\
        P                  P                  4      '       g   Q hVP                  VP                  4      R,          p\        VP                  V4       \        VP                  V4       R#   + '       g   i     L; irF  )r)   r   rb  r   r   r[   r  rY   r7  r  r  rb   r0   r>  r=  rc   rd   r   r  s   &&  rm   #test_ttest_ind_empty_1d_returns_nan0TestTTestInd.test_ttest_ind_empty_1d_returns_nan  s     B<<08MNNoobjjnbjjnE ON //"**R."**R.AC#u::;;;;jj $s+

C( ONs   6D**D:	r  c                0   VP                  R4      pVP                  WP                  R7      p\        P                  P                  4       ;_uu_ 4       pVP                  \        \        4       \        P                  ! WARR7      pRRR4       \        X\        P                  P                  4      '       g   Q hVP                  W#P                  R7      p\!        VP"                  V4       \!        VP$                  V4       R#   + '       g   i     L; i)r   r6   r>   Nr  r  rU   )rB  rY   r7   r   r"  r   r   r   r   r[   r  r7  r  r  r~   rb   r0   r>  r=  )rc   rW  r  rd   rK  r   r   r  s   &&&&    rm   test_ttest_ind_axis_size_zero*TestTTestInd.test_ttest_ind_axis_size_zero  s     HHYJJqJ(ZZ))++sJJ)+@A//!R0C , #u::;;;;FFC~6

N3 ,+s   3DD	c                F   VP                  R4      pVP                  R4      p\        P                  ! W#^R7      p\        V\        P                  P
                  4      '       g   Q hVP                  P                  R8X  g   Q hVP                  P                  R8X  g   Q hR# r  	rB  r[   r  r7  r  r  r>  r  r=  rc   rd   rK  rW  r   s   &&   rm    test_ttest_ind_nonaxis_size_zero-TestTTestInd.test_ttest_ind_nonaxis_size_zero  s}    
 HHYHHYooa+#u::;;;;}}""V+++zz6)))rp   c                F   VP                  R4      pVP                  R4      p\        P                  ! W#^R7      p\        V\        P                  P
                  4      '       g   Q hVP                  P                  R8X  g   Q hVP                  P                  R8X  g   Q hR# )rW   r>   N)rW   rJ   ry   r  r  r	  r	  s   &&   rm   2test_ttest_ind_nonaxis_size_zero_different_lengths?TestTTestInd.test_ttest_ind_nonaxis_size_zero_different_lengths  s}     HHYHHYooa+#u::;;;;}}""V+++zz6)))rp   r   NrW   rw   ry   r  r	  r   ry   )r   r   r   r   r.   r[   r  r	  r   r   r   r	  r	  r	  r  r   rB  r	  r	  r	  r   r   r   s   @rm   r	  r	  ^  s     u112N+ 3N+` [[: [[999,$*) [[0 hhy16:XXi0&9;<4<4
** *rp   r	  c                      a  ] tR tRt o ]P
                  P                  RRR7      R 4       t]P
                  P                  R4      R 4       t	Rt
V tR	# )
TestTTestIndFromStatsi  Tz"Other backends don't like integersr   c                   VP                  ^^.4      VP                  ^^.4      r2VP                  ^^.4      VP                  ^^.4      rTVP                  ^^.4      VP                  ^d^.4      rv\        P                  ! W$WcWW4       R# rW   N)rY   r[   r  )rc   rd   mean1mean2std1std2nobs1nobs2s   &&      rm   test_gh5686!TestTTestIndFromStats.test_gh5686  sy     zz1a&)2::q!f+=uZZA'QF);dzz3*-rzz3*/Eu""5dJrp   r	  c           
        VP                  R 4      pVP                  R4      pVP                  VP                  4      p\        P                  ! W"W2W#RR7      p\	        VP
                  V4       \	        VP                  V4       R# )r   r   Fr	  N)rY   rb   r[   r  r0   r>  r=  )rc   rd   zerosixr  r   s   &&    rm   %test_ttest_ind_from_stats_inputs_zero;TestTTestIndFromStats.test_ttest_ind_from_stats_inputs_zero&  se     zz"~jjnjj ((S38:s+

C(rp   r   N)r   r   r   r   r   r   r   r	  r   r	  r   r   r   s   @rm   r	  r	    sY     [[!!$'K " MKMK [[ QR) S)rp   r	  TzTest uses ks_1sampr5	  r	  c                    \         P                  P                  R 4      pV P                  VP	                  RR7      4      pV P                  VP	                  RR7      4      pVP                  ^dR7      p\        P                  ! W#RRR7      p\         P                  ! VP                  4      p\        P                  ! V\        P
                  ! 4       P                  4      P                  R8  g   Q h\        \         P                  ! Wd4      VRR7       \        P                  ! W2RRR7      p\         P                  ! VP                  4      p\        P                  ! V\        P
                  ! 4       P                  4      P                  R8  g   Q h\        \         P                  ! Wd4      VRR7       V P                  . RO4      V P                  R.4      r2\        P                  ! W#RR7      p\        V 4      V P                  8X  d   R	MR
p\        VP                   V P                  R4      VR7       \        VP                  V P                  R4      VR7       R# )l   bQ r  T)r  r?   rD  r  rE  r2   r	  r  r  gzNd?r  gJ?N)ri  rE   )ri  rW   rU   )rE   r   rw   )r   r  r  rY   r  r  r[   r  r=  r  r  r
   quantiler+   r   r/   r>  )rd   r  rf   rg   r@  r   r=  r  s   &       rm   test_ttest_uniform_pvaluesr	  2  s    ))


0C


3::::./A


3::::./AA
//!$R
8CZZ

#F>>&%--/"5"56==CCCBKK*AD9
//!$R
8CZZ

#F>>&%--/"5"56==CCCBKK*AD9
 ::i "**cU"3q
//!$
/C#B'2::545DCMM2::o#>TJCJJ

> :Frp   c                     VP                  VR 8H  4      pVP                  VR8H  4      pV ^ 8  V,          V ^ 8  V,          ,          pVP                  Wa^,          ^V^,          ,
          4      # )r  r  )rY   rP  )r  re  r  rd   r  r  r  s   &&&&   rm   _convert_pvalue_alternativer	  P  sa     ::cVm$Djj	)*G
a%4QUg-.A88AsA!G$$rp   r  r  c           	      J	   ^
^^r2p\         P                  P                  ^^
WV3R7      pV P                  V4      pV P	                  ^W#34      p\         P
                  ! WE^ R7      w  rg\         P
                  ! VR^ R7      w  r\         P
                  ! VR,          R4      w  r\        WhRR7       \        VR,          V
RR7       \        VP                  W#34       V P	                  V^V34      p\         P
                  ! WE^R7      w  rg\         P
                  ! VR^R7      w  r\         P
                  ! VR,          R4      w  r\        WhRR7       \        VR,          V
RR7       \        VP                  W34       V P	                  W^34      p\         P
                  ! WE^R7      w  rg\         P
                  ! VR^R7      w  r\         P
                  ! VR,          R4      w  r\        WhRR7       \        VR,          V
RR7       \        VP                  W34       \         P
                  ! V P                  . RO4      R4      w  r\        V P                  V4      V P                  V P                  4      4       \        WP                  R4      4       \         P
                  ! VR,          R4      w  r\         P
                  ! VR,          RRR7      w  r\        WRV 4      p\        VV4       \        W4       \         P
                  ! VR,          RR	R7      w  r\        WR	V 4      p\        VV4       \        W4       \        P                  ! R
R7      ;_uu_ 4        \         P
                  ! V P                  . RO4      R4      p\        VP                  V P                  V P                   4      4       \        VP"                  V P                  V P                   4      4       V P                  R\        P                   .RR..4      p\         P
                  ! VR4      p\        VP                  V P                  RV P                   .4      4       \        VP"                  V P                  RV P                   .4      4       RRR4       R#   + '       g   i     R# ; i)rO   r"  r>   r   ri  r  r   r  r  r  r}  r	  N)r   ry   ry   r  )ry   r   ry   )ry   ry   r   )r   r   r   r   r   r   rP  )r[   rX  r  rY   r  r  r/   r   r  r0   r  r!  r	  r   r  r>  rb   r=  )rd   r^  r_  n3rvn1r&  re  r  rf  p2rg  p3r  re  r  rH  pcr   r  s   &                  rm   test_ttest_1samp_newr	  Y  sq   
 b"BB::>>ar>=D::dD ggq"k"Gt15FBtRa0FBtG}b1FBB'BtHbu-B8$ggr1bk"Gt15FBtRa0FBtG}b1FBB'BtHbu-B8$ggrqk"Gt15FBtRa0FBtG}b1FBB'BtHbu-B8$ RZZ5r:DABFF1Irzz"&&12Azz"~&tG}b1FBT']BIFDA	$RY	;BArAT']BFCDA	$RVR	8BArA		"	"

< 8"=rzz"&&'9:

BJJrvv$67 zzB<#r34b)rzz2rvv,'?@

BJJBFF|$<= 
#	"	"	"s   "D%RR"	z(Only NumPy has nan_policy='omit' for nowr   c                    ^^
^r2p\         P                  P                  ^^
WV3R7      pV P                  V4      pV P                  VR	&   \         P
                  ! VR
,          RRR7      w  rV\         P
                  ! VR
,          RRRR7      w  rx\        WVRV 4      p	\        W4       \        Wu4       \         P
                  ! VR
,          RRRR7      w  rx\        WVRV 4      p	\        W4       \        Wu4       R# )rw   r"  r   r   r   r  re  r  N)r  :rW   r   N:r   rF   Nr	  )r[   rX  r  rY   rb   r  r	  r/   )
rd   r^  r_  r	  r	  r  rH  r  re  r	  s
   &         rm   test_ttest_1samp_new_omitr	    s    RBB::>>ar>=D::dD&&DtG}bVDFBT']B6)24DA	$RY	;BAAT']B6)/1DA	$RVR	8BAArp   r"  r#  r  c                    \         P                  P                  R 4      pVP                  R	R7      pV P                  V4      pRpV P                  VP                  R
R7      4      p\        P
                  ! \        VR7      ;_uu_ 4        \        P                  ! W$RR7       RRR4       V P                  VP                  RR7      4      p\        P                  ! W$RR7      pVP                  P                  R8X  g   Q hVP                  4       w  rgV P                  VRR7      pV P                  VRR7      p\        P                  ! W&RR7      pV P                  V P                  RV P                  R7      VP                  P                  4      p\!        VP                  V4       \        P                  ! W'RR7      p\!        VP                  V4       R#   + '       g   i     EL>; i)l   iI}pC r  z%`popmean.shape\[axis\]` must equal 1.r   )r&  r?   Nr>   g?r6   )rW   r  r  )rw   rE   r  rZ  )rw   rW   r  )rw   r  )r   r  r  rY   r   r   r   r[   r  r>  r  r  r4  r  r   r=  r/   )	rd   r  rf   r  r&  r   r5  r  r  s	   &        rm   test_ttest_1samp_popmean_arrayr	    sj    ))

 3
4C


$A


1A6Gjj45G	z	1	1!26 
2 jj45G


AR
8C==')))""$DA
qr"A
qr"A


Ar
2C
//"**T*<cjj>N>N
OCCJJ$


Ar
2CCJJ$! 
2	1	1s   
GG)	c                      a  ] tR tRt o ]P
                  P                  R4      R 4       tR tR t	R t
R tR tR	 tR
 tRtV tR# )TestDescribei  r  c           
        \        4       ;_uu_ 4       p\        P                  ! R R R7      ;_uu_ 4        VP                  \        R4       \
        P                  ! VP                  R4      R,          4      w  r4rVrxRRR4       RRR4       X^8X  g   Q h\        X^ ,          VP                  R4      4       \        V^,          VP                  R4      4       \        XVP                  R4      4       \        XVP                  VP                  4      4       \        XVP                  VP                  4      4       \        XVP                  VP                  4      4       R#   + '       g   i     L; i  + '       g   i     L; i)r}  r  r  r   Nr   )
r   r   r  r   r   r[   describerY   r0   rb   )	rc   rd   r   r  r  r  r  skkurts	   &&       rm   test_describe_scalar!TestDescribe.test_describe_scalar  s      Ckk(8<<JJ~'JK$)NN2::b>"3E$F!A1 = ! Avv1rzz#/1rzz#/2::c?+2::bff-.BJJrvv./bjj01 =< ! s#   !E7AE$	;E7$E4/E77F	c                   VP                  VP                  R4      VP                  RR4      34      p^pVP                  . RO4      VP                  . R	O4      3pVP                  . R
O4      pVP                  . RO4      pVP                  R.^,          4      pVP                  R.^,          4      p\        P
                  ! V4      w  rrrW8X  g   Q h\        V
^ ,          V^ ,          4       \        V
^,          V^,          4       \        W^VP                  VP                  4      P                  ,          R7       \        W^VP                  VP                  4      P                  ,          R7       \        W4       \        W4       \        P
                  ! VP                  ^R7      w  rrrW8X  g   Q h\        V
^ ,          V^ ,          4       \        V
^,          V^,          4       \        W^VP                  VP                  4      P                  ,          R7       \        W^VP                  VP                  4      P                  ,          R7       \        W4       \        W4       R# )r   r   H,p ?r  r>   Nr  rE   r   r   r   r   r   r   r   r   r   ffffff?r	  r	  r	  )rG  rG  rG  rG  TUUUUU)r  r  r~   rY   r[   r	  r0   r/   r   r7   epsr   rc   rd   rf   ncmmcmcvcskckurtcr  r  r  r  r	  r	  s   &&             rm   test_describe_numbers"TestDescribe.test_describe_numbers  s   IIrwwv(;<=zz*+RZZ8H-IJZZ,-ZZ,-jj-.23

./!34 %q 1qRww1s1v&1s1v&A(9(=(=$=>A(9(=(=$=> $ %qss ;qRww1s1v&1s1v&A(9(=(=$=>A(9(=(=$=> $rp   c                .   \         P                  ! R 4      p\         P                  V^	&   ^	Rr2RpRpRpR	p\        P                  ! VRR7      w  rrr\        W4       \        W4       \        W4       \        W4       \        W4       \        W^R7       R# )
r   r   r   rZ  r   r   rW  N)r   r   gGz)r   r   rb   r[   r	  r   r   )rc   rf   r	  r	  r	  r	  r	  r	  r  r  r  r  r	  r	  s   &             rm   describe_nan_policy_omit_test*TestDescribe.describe_nan_policy_omit_test  s    IIcNvv!jC# %qV DqRQRQQ!"*!$r:rp   c                   VP                  R 4      pVP                  V^	8H  VP                  V4      p\        V4      '       dG   \        P
                  ! \        RR7      ;_uu_ 4        \        P                  ! VRR7       RRR4       ME\        P
                  ! \        RR7      ;_uu_ 4        \        P                  ! VRR7       RRR4       \        P                  ! VRR7      w  r4rVrxVP                  VP                  4      R,          p	V^
8X  g   Q h\        V^ ,          V	4       \        V^,          V	4       \        WY4       \        Wi4       \        Wy4       \        W4       \        V4      '       d   V P                  4        M\        V4      '       dG   \        P
                  ! \        RR7      ;_uu_ 4        \        P                  ! VRR7       RRR4       MGR	p
\        P
                  ! \        V
R7      ;_uu_ 4        \        P                  ! VRR7       RRR4       R
p
\        P
                  ! \        V
R7      ;_uu_ 4        \        P                  ! VRR7       RRR4       R#   + '       g   i     EL; i  + '       g   i     EL; i  + '       g   i     L; i  + '       g   i     L; i  + '       g   i     R# ; i)r   not supported for lazy arraysr   r   r   Nr   r  r   z8nan_policy='omit' is incompatible with non-NumPy arrays.r   r   r   )r   rP  rb   r(   r   r   r&  r[   r	  r   rY   r0   r)   r	  )rc   rd   rf   r  r  r  r  r	  r	  r  r  s   &&         rm   test_describe_nan_policy_other+TestDescribe.test_describe_nan_policy_other
  s   IIcNHHQT2661%y0OPPqW5 QP z1PQQqW5 R !&q[ IqRjj $Bww1s#1s# "B<<..01y0OPPqV4 QP QGz99qV4 : 1]]:W55NN12 657 QPP RQQ  QP :9 655s<   'I0-J>JJ+J>0J	J	J(	+J;	>K	c                t    \         P                  ! \        P                  ! R 4      4      pRp\	        W4       R# )r8   N)r  minmaxr^   variancer  r  )r[   r	  r   r   r   )rc   r  r@  s   &  rm   test_describe_result_attributes,TestDescribe.test_describe_result_attributes-  s'     		".S
F/rp   c                r   VP                  VP                  R4      VP                  RR4      34      p^pVP                  . RO4      VP                  . RO4      3pVP                  . R	O4      pVP                  . R
O4      pVP                  R.^,          4      pVP                  R.^,          4      p\        P
                  ! V^ R7      w  rrrW8X  g   Q h\        V
^ ,          V^ ,          4       \        V
^,          V^,          4       \        W4       \        W4       \        W4       \        W4       R# )r   r   r	  rM  Nr  r	  r	  r	  r	  )Q?r 
  r 
  r 
  r	  r  r  r~   rY   r[   r	  r0   r/   r	  s   &&             rm   test_describe_ddofTestDescribe.test_describe_ddof4  s    IIrwwv(;<=zz*+RZZ8H-IJZZ,-ZZ01jj-.23

./!34 %qq 9qRww1s1v&1s1v& $rp   c                B   VP                  VP                  R4      VP                  R	R4      34      p^pVP                  R4      VP                  R4      3pVP                  R4      pVP                  R4      pVP                  R4      pVP                  R
4      p\        P
                  ! VRR7      w  rrrW8X  g   Q h\        V
^ ,          V^ ,          4       \        V
^,          V^,          4       \        W4       \        W4       \        W4       \        W4       R# )r   r   r   r	  ga+?gE,p ?Nr>   r  r	  gUUUUUUr
  r	  s   &&             rm   test_describe_axis_none$TestDescribe.test_describe_axis_noneE  s    IIrwwv(;<= zz#

30ZZ*+ZZ+,jj+,

./ !&qt <qRww1s1v&1s1v& $rp   c                    R p\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! VP                  . 4      4       RRR4       R#   + '       g   i     R# ; i)zThe input must not be empty.r   N)r   r   r   r[   r	  rY   rc   rd   r  s   && rm   test_describe_empty TestDescribe.test_describe_empty[  s;    0]]:W55NN2::b>* 6555s   &AA(	r   N)r   r   r   r   r   r   r   r	  r	  r	  r	  r	  r
  r
  r	
  r   r   r   s   @rm   r	  r	    sQ     [[ VW2 X2%4;"!3F0%"%,+ +rp   r	  c                   n   a  ] tR tRt o ]P
                  P                  R. RO4      R 4       tR tRt	V t
R# )NormalityTestsia  r  c                   V P                   p\        \        V4      pVP                  V P                  ^ ,          4      pVP                  V P                  ^,          4      p/ pVR9   dU   VR9   d8   VR8X  d
   V^,          M^V^,          ,
          pVR8X  d
   ^V,
          MTpWR&   M\
        P                  ! R4       VP                  R	4      ^,          pV! V3/ VB p	V	w  r\        W4       \        W4       \        V	R
VR7       R# )ry   r  skewtestr  z,`alternative` not available for `normaltest`r  N>   r  r  >   r
  kurtosistest)rZ  rU   ry   rW   rE   r   rZ  rU   ry   rW   rE   r   rZ  rU   ry   rW   rE   r   rZ  rU   ry   rW   rE   r   r  )		test_namerj  r[   rY   case_refr   r  r/   r   )rc   r  rd   r
  r  ref_statisticr`  r@  rf   r   res_statistic
res_pvalues   &&&         rm   test_against_RNormalityTests.test_against_Rc  s     NN	5),zz$--"23ZZa 01
--88-8F-BZ\*UV,
-6*-DQz\*
(3}%JKJJ./2q#F#$'!5
/C!8R@rp   c                   \        \        V P                  4      pVP                  R 4      pVP	                  VP
                  VP                  R7      pVP                  V^8H  WC4      p\        P                  ! RR7      ;_uu_ 4        V! V4      p\        VP                  V4       \        VP                  V4       RRR4       R#   + '       g   i     R# ; i)r  r6   r}  r~  N)rj  r[   r
  r   rY   rb   r7   rP  r   r  r0   r>  r=  )rc   rd   r  rf   r  r   s   &&    rm   test_nanNormalityTests.test_nan  s    5$..1IIcNjjqwwj/HHQ"Wc%[[**1+CCMM3/CJJ, +***s   5CC	r   Nrn  )r   r   r   r   r   r   r  r
  r
  r   r   r   s   @rm   r
  r
  a  s6     [[],LMA NA<	- 	-rp   r
  c                   4   a  ] tR tRt o RtRtR tR tRtV t	R# )TestSkewTesti  r
  c                    \         P                  P                  ^R^{R7      pVP                  V4      p\         P                  ! VRR7      P
                  p\        WAP                  RVP                  R7      RR7       R	# )
rW   ri  )rK  r  r  r  r  r   r6   g?̔>rE  N)r[   skewnormr  rY   r
  r=  r/   r7   )rc   rd   r  a1_xpr  s   &&   rm   test_intuitiveTestSkewTest.test_intuitive  s[    ^^!%cB

2~~e;BBjjEKKj@tLrp   c                   \         P                  ! VP                  R 4      4       VP                  R4      p\        V4      '       d   \        MRp\
        P                  ! \        VR7      ;_uu_ 4        \         P                  ! V4      pVP                  VP                  4      p\        VP                  V4       \        VP                  V4       RRR4       R#   + '       g   i     R# ; i)r   r   z1`skewtest` requires at least 8 valid observationsr   N)r[   r
  r   r)   r   r   rb  r   rY   rb   r0   r>  r=  )rc   rd   rf   r  r   r  s   &&    rm   "test_skewtest_too_few_observations/TestSkewTest.test_skewtest_too_few_observations  s     	ryy~&IIcN,4RLL(K 	\\,G<<..#C**RVV$CCMM3/CJJ,	 =<<<s   4ACC-	r   N)gvO?gbH`?)
r   r   r   r   r
  r
  r
  r"
  r   r   r   s   @rm   r
  r
    s     I9HM- -rp   r
  c                   :   a  ] tR tRt o RtRtR tR tR tRt	V t
R# )	TestKurtosisTesti  r
  c                    \         P                  P                  R ^{R7      pVP                  V4      p\         P                  ! VRR7      P
                  p\        WAP                  RVP                  R7      RR7       R# )	ri  )r  r  r  r  r   r6   rD  rE  N)r[   laplacer  rY   r
  r=  r/   r7   )rc   rd   r  a2_xpr  s   &&   rm   r
  TestKurtosisTest.test_intuitive  s[    ]]E<

2!!%Y?FFjjEKKj@uMrp   c           
     (   . ROp\         P                  ! \        V4       UUu. uF  w  r4\         P                  ! WC4      NK  	  upp4      pVP	                  WQP
                  R7      p\        P                  ! V4      ^,          R8  g   Q hR# u uppi )rC  r6   r  N)
rC  ry   :   rJ   ry   )      ry   ry      )r   hstack	enumerater~   rY   r   r[   r
  )rc   rd   r  r  rj  rf   s   &&    rm   test_gh9033_regression'TestKurtosisTest.test_gh9033_regression  so     7II61BC1Brwwq}1BCDJJq

J+!!!$Q'$... Ds   !B
c                   \         P                  ! VP                  R 4      4       \        V4      '       d   \        MRp\
        P                  ! \        VR7      ;_uu_ 4        \         P                  ! VP                  R4      4      pVP                  VP                  4      p\        VP                  V4       \        VP                  V4       RRR4       R#   + '       g   i     R# ; i)r8   z(`kurtosistest` requires at least 5 validr   r   N)r[   r
  r   r)   r   r   rb  r   rY   rb   r0   r>  r=  )rc   rd   r  r   r  s   &&   rm   &test_kurtosistest_too_few_observations7TestKurtosisTest.test_kurtosistest_too_few_observations  s     	299S>*,4RLL(B 	\\,G<<$$RYYr]3C**RVV$CCMM3/CJJ,	 =<<<s   #A-CC+	r   N)gglg2J@?)r   r   r   r   r
  r
  r
  r1
  r4
  r   r   r   s   @rm   r%
  r%
    s$     I:HN/- -rp   r%
  c                   .   a  ] tR tRt o RtRtR tRtV tR# )TestNormalTesti  
normaltestc                   \         P                  ! VP                  R 4      4       \        P                  ! \
        4      ;_uu_ 4        \         P                  ! VP                  R4      4      pVP                  VP                  4      p\        VP                  V4       \        VP                  V4       RRR4       R#   + '       g   i     R# ; i)r   r   N)r[   r8
  r   r   rb  r   rY   rb   r0   r>  r=  r	  s   &&  rm   test_too_few_observations(TestNormalTest.test_too_few_observations  s    2' \\,--""299R=1C**RVV$CCMM3/CJJ,	 .---s   A-B??C	r   N)gاc@g?)	r   r   r   r   r
  r
  r:
  r   r   r   s   @rm   r7
  r7
    s     I9H	- 	-rp   r7
  c                      a  ] tR tRt o ]P
                  P                  ^ 4       ]P
                  P                  ^^
4      w  tt	]
P                  P                  R. RO4      R 4       tR tR tRtV tR# )	TestRankSumsi  r  c                    \         P                  ! V P                  V P                  VR 7      P                  p\         P
                  ! V P                  V P                  RVR7      P                  p\        W#4       R# )r  F)use_continuityr  N)r[   ranksumsrf   rg   r=  mannwhitneyur
   )rc   r  r  r  s   &&  rm   test_ranksums_result_attributes,TestRankSums.test_ranksums_result_attributes  sZ     ~~dffdff*577=v 	!!$&&$&&.9;;A6 	#rp   c                t    \         P                  ! V P                  V P                  4      p\	        VR4       R# r  )r[   r@
  rf   rg   r   ry  s   & rm   test_ranksums_named_results(TestRankSums.test_ranksums_named_results  s%    nnTVVTVV,C!89rp   c                    \        \        R R7      ;_uu_ 4        \        P                  ! V P                  V P
                  RR7       RRR4       R#   + '       g   i     R# ; i)z`alternative` must be 'less'r   r   r  N)r   r   r[   r@
  rf   rg   r|  s   &rm   r  "TestRankSums.test_input_validation  s8    :-KLLNN466466x@ MLLLs   .AA#	r   Nr
  )r   r   r   r   r   r  r  r  rf   rg   r   r   r  rB
  rE
  r  r   r   r   s   @rm   r=
  r=
    sc     IINN199>>!R DAq[[],LM$ N$:A Arp   r=
  c                   j   a  ] tR tRt o R t]! RR7      R 4       t]! RRR7      R	 4       tR
 tRt	V t
R# )TestJarqueBerai  c                    . ROpVP                  V4      pVP                  RR.4      p\        P                  ! V4      p\        VP                  V^ ,          4       \        VP
                  V^,          4       R# )g8MK~?gq"?gPHK?N)g8MK~Ŀg/?g6r=TgGg!J_l )rY   r[   jarque_berar/   r>  r=  )rc   rd   rf   r  r   s   &&   rm   test_jarque_bera_against_R)TestJarqueBera.test_jarque_bera_against_R  s^    
;JJqMjj*O<="s1v.

CF+rp   Tr  c                   \         P                  P                  R 4       \         P                  P                  ^ ^R4      p\        P
                  ! \        V4      4      ;pw  rE\        P
                  ! \        V4      4      ;pw  rx\        P
                  ! VP                  ^R4      4      ;p	w  rYGu;8X  d?   T
u;8X  d7   VP                  u;8X  d%   VP                  u;8X  d   V	P                  8X  g   Q h Q hYXu;8X  d?   Tu;8X  d7   VP                  u;8X  d%   VP                  u;8X  d   V	P                  8X  g   Q h Q hR# )r  r^  P  N)r   r  r  r  r[   rL
  r:  tupler]   r>  r=  )rc   rd   rf   jb_test1JB1r  jb_test2JB2r	  jb_test3JB3r	  s   &&          rm   test_jarque_bera_array_like*TestJarqueBera.test_jarque_bera_array_like  s     			y!IIQ6*"..tAw7773"..uQx8873"..qyyE/BCC73bSbH$6$6b(:L:LbPXPbPbbbbbbV2VVHOOVxVVVVVrp   array_api_strictzNoisy; see TestSkewr  c                l   VP                  . 4      p\        P                  ! \        \        R 7      ;_uu_ 4        \
        P                  ! V4      pVP                  VP                  4      p\        VP                  V4       \        VP                  V4       RRR4       R#   + '       g   i     R# ; ir  )rY   r   rb  r   r   r[   rL
  rb   r0   r>  r=  )rc   rd   rf   r   r  s   &&   rm   %test_jarque_bera_too_few_observations4TestJarqueBera.test_jarque_bera_too_few_observations  sp    JJrN\\,4IJJ##A&C**RVV$CCMM3/CJJ,	 KJJJs   AB""B3	c                   \         P                  P                  R R7      pVP                  VP                  RR7      4      p\        P
                  ! VRR7      p\        P
                  ! VP                  VR4      4      p\        VP                  VP                  4       \        VP                  VP                  4       \        P
                  ! V^R7      p\        P
                  ! VR,          4      w  rg\        P
                  ! VR,          4      w  r\        VP                  VP                  Wh.4      4       \        VP                  VP                  Wy.4      4       \        P
                  ! VP                  ^ R7      p
\        VP                  V
P                  4       \        VP                  V
P                  4       R# )	iKr  r  Nr>   )rE   r  r  rq  rr  )r   r  r  rY   r[   rL
  r]   r0   r>  r=  r/   r  r   )rc   rd   r  rf   r   r  s0r  s1r  resTs   &&         rm   r  TestJarqueBera.test_axis  s-   ii###3JJszzwz/0-

1e 45s}}5

CJJ/*""1T7+""1T7+rxx'9:

BHHbX$67  1-t~~6

DKK0rp   r   N)r   r   r   r   rM
  r   rX
  r\
  r  r   r   r   s   @rm   rJ
  rJ
    sM     , d#
W $
W (1FG- H-1 1rp   rJ
  c                   X   a  ] tR tRt o . R
Ot. ROt^tR tR tR t	R t
R tR tRtV tR	# )TestMannWhitneyUi.  c                   \         P                  ! V P                  V P                  R R7      w  r\         P                  ! V P                  V P                  RR7      w  r4\         P                  ! V P                  V P                  RR7      w  rV\         P                  ! V P                  V P                  R R7      w  rx\	        W$4       \	        Wh4       \        W&8g  4       \	        VR4       \	        V^f4       \	        VR4       \	        V^f4       \        VRV P                  R7       \        VRV P                  R7       R# )r  r  r    g=_A?r  glPz.?Nr[   rA
  rZ   Yr   r   r	   r  	rc   u1r  u2r	  u3r	  u4p4s	   &        rm   test_mannwhitneyu_one_sided,TestMannWhitneyU.test_mannwhitneyu_one_sided@  s    ##DFFDFFG##DFFDFF	J##DFFDFF	J##DFFDFFGRRRRRRB 1t?O?OPB 3AQAQRrp   c                8   \         P                  ! V P                  V P                  R R7      w  r\         P                  ! V P                  V P                  R R7      w  r4\	        W$4       \	        VR4       \	        V^f4       \        VRV P                  R7       R# )r  r  rf
  glPz.?r  Nr[   rA
  rZ   rh
  r   r	   r  rc   rj
  r  rk
  r	  s   &    rm   test_mannwhitneyu_two_sided,TestMannWhitneyU.test_mannwhitneyu_two_sidedP  sp    ##DFFDFFL##DFFDFFLRRRB 2(,(8(8	:rp   c                   \         P                  ! V P                  V P                  R RR7      w  r\         P                  ! V P                  V P                  R RR7      w  r4\         P                  ! V P                  V P                  R RR7      w  rV\         P                  ! V P                  V P                  R RR7      w  rx\	        W$4       \	        Wh4       \        W&8g  4       \	        VR4       \	        V^f4       \	        VR4       \	        V^f4       \        VRV P                  R7       \        VRV P                  R7       R# )	Fr  r  r  rf
  gii5?r  g22?Nrg
  ri
  s	   &        rm   &test_mannwhitneyu_no_correct_one_sided7TestMannWhitneyU.test_mannwhitneyu_no_correct_one_sidedZ  s    ##DFFDFFE068##DFFDFFE09;##DFFDFFE09;##DFFDFFE068 	RRRRRRB 1t?O?OPB 4$BRBRSrp   c                <   \         P                  ! V P                  V P                  R RR7      w  r\         P                  ! V P                  V P                  R RR7      w  r4\	        W$4       \	        VR4       \	        V^f4       \        VRV P                  R7       R# )Fr  r  rf
  g22?r  Nrr
  rs
  s   &    rm   &test_mannwhitneyu_no_correct_two_sided7TestMannWhitneyU.test_mannwhitneyu_no_correct_two_sidedn  s|    ##DFFDFFE0;=##DFFDFFE0;= 	RRRB 4(,(8(8	:rp   c                r   \         P                  ! . R NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NR NRNR NR NRNR NR NRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NR NR NR NR NR NR NRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR N4      p\         P                  ! . R NR NR NR NR NR NR NRNR NRNR NR NR NR NRNR NR NR NRNR NR NR NR NR NRNR NR NRNR NR NR NR NR NR NR NR NR NR NRNR NRNR NR NR NR NR NR NRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NR NR NRNRNR NR NRNR NR NRNR NRNR NR NR NR NRNRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NR NR NRNRNRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NRNR NR NR NR NRNR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NRNR NR NR NR NR NR N4      p\        \        P                  ! WRR7      R4       \        \        P                  ! WRR7      R	4       \        \        P                  ! WRR7      R
4       R# )r   r   r   r  r  r  r  N)     @g ?չ>)r}
  g&)E?)r}
  g?չ?)r   r   r
   r[   rA
  r  s   &  rm   test_mannwhitneyu_ones'TestMannWhitneyU.test_mannwhitneyu_onesz  s   HH .b ." .b ." .b ." .b ." .b ." .b ." .b ." ... ."$.&(.*,..0.24.68.:<.>@.BD.FH.JL... ."$.&(.*,..0.24.68.:<.>@.BD.FH.JL. . . !. #%. '). +-. /1. 35. 79. ;=. ?A. CE. GI. KM. 	. 	. !	. #%	. ')	. +-	. /1	. 35	. 79	. ;=	. ?A	. CE	. GI	. KM	.
 .
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 KM. . . !. #%. '). +-. /1. 35. 79. ;=. ?A. CE. GI. KM. . . !. #%. '). +-. /1. 35. 79. ;=. ?A. CE. GI. KM. . . !. #%. '). +-. /1. 35. 79. ;=. ?A. CE. GI. KM. . . !. #%. '). +-. /1. 35. 79. ;=. ?A. CE. GI. KM. . . !. #%. '). +-. /1. 35. 79. ;=. ?A. CE. GI. KM. . . !. #%. '). +-. /1. 35. 79. ;=. ?A. CE. GI. KM. . . !. #%. '). +-. /1. 35. 79. ;=. ?A. CE. GI. KM. . . !. #%. '). +-. /1. 35. 79. ;=. ?A. CE. GI. KM. . . !. #%. '). +-. /1. 35. 79. ;=. ?A. CE. GI. KM. . . !. #%. '). +-. /1. 35. 79. ;=. ?A. CE. GI. KM.  !.  !.  !!.  #%!.  ')!.  +-!.  /1!.  35!.  79!.  ;=!.  ?A!.  CE!.  GI!.  KM!." #." #." !#." #%#." ')#." +-#. /& HH &b &" &b &" &b &" &b &" &b &" &b &" &b &" &&& &"$&&(&*,&.0&24&68&:<&>@&BD&FH&JL&&& &"$&&(&*,&.0&24&68&:<&>@&BD&FH&JL& & & !& #%& ')& +-& /1& 35& 79& ;=& ?A& CE& GI& KM& 	& 	& !	& #%	& ')	& +-	& /1	& 35	& 79	& ;=	& ?A	& CE	& GI	& KM	&
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  r   r  s   &  rm   #test_mannwhitneyu_result_attributes4TestMannWhitneyU.test_mannwhitneyu_result_attributes  s+    ,
  VDC,rp   r   N)g	U3@g^3@gt3@g]o5@gzS4@gt< 4@gM	X3@gXmCk4@gLo&3@gfɘ2@g{m;^3@ga A$|3@gMѢ_4@g#3@g19T_3@ggC2@gqR4@gKk/4@g܁3@gZ2@g_
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x4@g3#л5@g;VND1@g >H2@gr4@gyܤ2@g?4@g=bɇ3@)gpG3@gL:j0@g2@gJNnC1@gR;`(3@g+Pi,2@g6:Z2@gZ"3=2@gF	uSa	3@gXҀ2@gX3^83@g21@gJ2@gZ)E2@gU83@g50@gԆ3@gFz33@gz3@gڴ3@)r   r   r   r   rZ   rh
  r  ro
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  r   r   r   s   @rm   rd
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  .  sA     	-A	NA KS :T(
:)7V- -rp   rd
  c                     . ^N^ N^N^N^N^N^ N^N^ N^ N^ N^N^N^ N^ N^ N^N^N^N^ N^ N^ N^ N^ N^ N^ N^ N^N^ N^ N^ N^ N^ N^Np . RNRNRNRNRNRNRNRNR	NR
NRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNp\        \        P                  ! W4      ^ ,          R^4       R p\        P                  ! W4      p\        W24       \	        VP
                  VP                  4       R# )!rW   g-@g+@g(@rm  r  r  g333333@ffffff@g333333@r  r  皙	@r   r  rt   r  ffffff@ @333333?r2   ?rt  r  r@  rE  ro  r1   r4  rD  g/"?Nr<  )r   r[   pointbiserialrr   r   r;  r>  )rf   rg   r@  r   s       rm   test_pointbiserialr
    sU   	 	1 	Q 	q 	 	1 	Q 	q 	 	1 	Q 	q 	 	1 	Q 	q 	 	1 	Q 	q 	 	1 	Q 	q 	 	1 	Q 	q 	 		
					A	& 	&d 	&4 	& 	&S 	& 	&S 	& 	&S 	& 	&S 	& 	&S 	&		&	&	&	&	& 	&!$	&%(	&),	&-0	&14	&58	&9<	&=@	&		&	&	&	&	& 	&!$	&A ,,Q215wB +J


q
$C(#--0rp   c                  8   \         P                  ! . RO4      p \        P                  ! V 4      p. ROp\	        V^ ,          V4       \         P                  ! . RO4      p\        P                  ! V4      p\         P                  ! . RO4      p\	        V^ ,          V4       \        P                  ! W4      w  rV\        WQ^ ,          4       \        Wd^ ,          4       \        P                  ! WV 4      w  rVp\        WQ^ ,          4       \        Wd^ ,          4       \        Wq^ ,          4       \         P                  ! ^4      p \         P                  ! . RO. RO.4      p\        \        P                  ! V ^V ,          4      V^R7       \        ^^4      p	\         P                  ! . R	O4      p
\         P                  ! W4      p\         P                  ! . R
O4      p\         P                  ! W4      p\        P                  ! V4      p\        V^ ,          V^R7       R# )ry   rW  N)ry   rE   r   )rJ   rZ  rJ   )ry   r   rz   rI   )r  ry   ry   r  )㪪@I?g&>ڿr
  r
  )5@㪪@gIr
  r
  )rw   rP   rI   r   rE   rE   )g_v	@g1%?g"u?gZӼ?g!u @gq&@)
r   r   r[   obrientransformr
   r   r   r   r  r  )r  re  r  r  rf  rK  rW  rj  r  valuesrepsr  transformed_valuess                rm   test_obrientransformr
    s   	)	B			r	"BHBqE8$	,	B			r	"Bxx'HBqE8$   (DAqEqE ##BB/GA!qEqEqE 
1BXXDFHIF e33B"=vqQ 1b\F88'(D99V"D #< =yy+2H""4(FfQi1=rp   r7   r  r  weightsc           	      >   T;'       g    V P                   p\        V4      ^8X  d   Vw  rxMVw  rypV P                  WsR7      pV P                  WR7      pVe   V P                  WSR7      MTp\        V4      ^8X  d   V3MVX	3pV! VRVRVRV/ p
\        WVR7       R# )rE   r6   Nr?   r7   r
  r  )r   r   rY   r/   )rd   mean_funr?   r7   r  r
  r?  
array_liker  re  rf   s   $$$$$$*    rm   check_equal_xmeanr
    s     RZZE
4yA~"
G!%
wJ4Jjjj.G292Ebjjj.7GINJ=QD$@T@@@AAT*rp   c                  8    \        V R \        P                  /VB # r
  )r
  r[   r  r?  r@  s   *,rm   check_equal_gmeanr
        dCU[[CFCCrp   c                  8    \        V R \        P                  /VB # r
  )r
  r[   hmeanr
  s   *,rm   check_equal_hmeanr
    r
  rp   c                  8    \        V R \        P                  /VB # r
  )r
  r[   pmeanr
  s   *,rm   check_equal_pmeanr
     r
  rp   c                      a  ] tR tRt o ]P
                  P                  R4      R 4       tR t]P
                  P                  R4      ]P
                  P                  R4      R 4       4       t	]P
                  P                  R4      R 4       t
R	 tR
 t]P
                  P                  R4      R 4       tR t]P
                  P                  R4      R 4       t]! RRR7      R 4       tR tR tR t]R 4       tRtV tR# )	TestHMeani  r  c                ,    . ROp^ p\        W#VR7       R# rW   r  N)rW   ry   rE   r
  rc   rd   rK  r  s   &&  rm   test_0TestHMean.test_0  s    !,rp   c                R    . ROpRp\        W#VR7       . ROpRp\        W#VR7       R# )rO   g=b#A@r  NrX  r  gQ?r
  r
  s   &&  rm   test_1dTestHMean.test_1d  s*    5!,:!,rp   r  c                V    \         P                  ! ^^ .4      pRp\        W#VRR7       R# )rW   r   rd   r  Nr   r   r
  r
  s   &&  rm   test_1d_with_zeroTestHMean.test_1d_with_zero  s'     HHaV!#6rp   r	  c           	         \         P                  ! . RO4      pRp\        P                  ! \        VR7      ;_uu_ 4        \        W!P                  VRR7       RRR4       R#   + '       g   i     R# ; i)rW   z$The harmonic mean is only defined...r   r   r
  NrW   ry   rU   )r   r   r   rb  r   r
  rb   )rc   rd   rK  r  s   &&  rm   test_1d_with_negative_value%TestHMean.test_1d_with_negative_value  sG     HHZ 8\\.88aBS9 9888s   A""A3	c                b    . RO. RO. RO.pRp\        \        P                  ! V4      W1R7       R# )rO   gmWUC@r  NrO   r  r  r  r  rD  rY  rH  r!  r  r`  x   )r
  r   r   r
  s   &&  rm   test_2dTestHMean.test_2d'  s'    /1DE"((1+w6rp   c                h    . RO. RO. RO.p\         P                  ! . RO4      p\        W#^ VR7       R# )rO   r?   rd   Nr
  r
  r
  )U|ϊ6@g4.=C@JQ6LsJ@E]P@r
  r
  s   &&  rm   test_2d_axis0TestHMean.test_2d_axis0-  s+    /1DE((OP!14rp   c                h    . RO. RO. RO.p\         P                  ! . RO4      p\        W#^ VR7       R# )rO   r
  NrO   ry   r  r  r
  r
  )r
  r   r
  r
  r
  r
  s   &&  rm   test_2d_axis0_with_zero!TestHMean.test_2d_axis0_with_zero3  s+    .0CD((GH!14rp   c                h    . RO. RO. RO.p\         P                  ! . RO4      p\        W#^VR7       R# )rO   r
  Nr
  r
  r
  )g3333333@O@y@Y@r
  r
  s   &&  rm   test_2d_axis1TestHMean.test_2d_axis19  s+    /1DE((<=!14rp   c                h    . RO. RO. RO.p\         P                  ! . RO4      p\        W#^VR7       R# )rO   r
  Nr
  r
  r
  )r   r
  r
  r
  r
  s   &&  rm   test_2d_axis1_with_zero!TestHMean.test_2d_axis1_with_zero?  s+    .0CD((;<!14rp   T,array-likes only supported for NumPy backendr   c                    . ROp. ROpRp\         P                  ! W#R7      p\        V\        P                  ! V4      RR7       R# )rE   r   r
  h㈵>r  NrE   rO   rz   rO   rw   r   )r[   r
  r/   r   rY   rc   rd   rK  r
  r  r   s   &&    rm   test_weights_1d_listTestHMean.test_weights_1d_listE  s8      kk!-RZZ0t<rp   c                    \         P                  ! . RO4      p\         P                  ! . RO4      p^p\        W$VRVR7       R# )rE   r
  r
  r  rd   Nr
  r
  )r   rY   r
  rc   rd   rK  r
  r  s   &&   rm   test_weights_1dTestHMean.test_weights_1dU  s3     JJz"**Z(!gDRHrp   c           	         \         P                  ! ^^.^
^.^^..4      p\         P                  ! ^
^.^^.^^..4      p\         P                  ! ^^.4      p\        W$^ VRVR7       R# )rE   r
  r?   r
  r  rd   Nr
  r
  s   &&   rm   test_weights_2d_axis0TestHMean.test_weights_2d_axis0]  sh     HHq!fr1g1v./((RGaVaV45((Aq6"!1gDRPrp   c           	         \         P                  ! . RO. RO.4      p\         P                  ! . RO. RO.4      p\         P                  ! ^^.4      p\        W$^VRVR7       R# )rE   r
  r
  Nr
  rJ   rJ   rJ   r
  r  r
  r
  s   &&   rm   test_weights_2d_axis1TestHMean.test_weights_2d_axis1e  sL     HHj),-((J	23((Aq6"!1gDRPrp   c           	         \         P                  ! . RO4      p\         P                  P                  . RO. ROR7      p^p\         P                  p\        W$VR\         P                  VR7       R# )rE   r  r
  r
  r  r7   rd   NrE   rO   rz   r  rO   rw   r   r  ry   ry   ry   rW   )r   r   rx  r
  r   r
  s   &&   rm   test_weights_masked_1d_array&TestHMean.test_weights_masked_1d_arraym  sM     HH^$%%++n<+@UU!gD "

r	3rp   r   N)r   r   r   r   r   r   r   r
  r
  r
  r
  r
  r
  r
  r
  r
  r   r
  r
  r
  r
  r%   r
  r   r   r   s   @rm   r
  r
    s/    [[ WX- Y-
- [[ WX[[ VW7 X Y7
 [[:::75 [[ WX5 Y5
5 [[ WX5 Y5
 =
=	
=IQQ 3 3rp   r
  c                   :  a  ] tR tRt o ]P
                  P                  R4      R 4       tR tR t	R t
R tR t]P
                  P                  R4      R	 4       t]P
                  P                  R
4      R 4       t]! RRR7      R 4       tR t]R 4       tRtV tR# )	TestGMeaniy  z<ignore:divide by zero encountered in log:RuntimeWarning:daskc                ,    . ROp^ p\        W#VR7       R# r
  r
  r
  s   &&  rm   r
  TestGMean.test_0{  s     !,rp   c                    . ROpRp\        W#VR7       . ROp\        ^R	4      p\        W#RVR7       \        . RO\        4      p\        ^R	4      p\        W#VP                  VR7       R# )
rO   gsŤF@r  ri  r  rd   )r7   rd   NrX  r  r  )r
  r   r   r   r
  s   &&  rm   r
  TestGMean.test_1d  s[    5!,w/!5R8,(w/!BJJ2>rp   c                :    . RO. RO. RO.pRp\        W#VR7       R# )rO   g/,$qJ@r  Nr
  r
  r
  r
  r
  s   &&  rm   r
  TestGMean.test_2d  s    /1DE!,rp   c                    . RO. RO. RO.p\         P                  ! . RO4      p\        W#^ VR7       \        . R	O. R	O. R	O.4      p\        . R	O4      p\        W#^ RVR7       R# )
rO   r
  ri  r?   r  rd   Nr
  r
  r
  )g4@A@g5H@g`8|wЭN@gm~&+R@r  r   r   r
  r
  s   &&  rm   r
  TestGMean.test_2d_axis0  sT    /1DE((NO!14<|<=%!15R@rp   c                    . RO. RO. RO.p\         P                  ! . RO4      p\        W#^VR7       \        . R	O. R	O. R	O.4      p\        ^R
4      p\        WDV.4      p\        W#^RVR7       R# )rO   r
  ri  r
  Nr
  r
  r
  )gD" 6"6@gcP@g
ҧZ@r  r  )r   r   r
  r   )rc   rd   rK  r  r  s   &&   rm   r
  TestGMean.test_2d_axis1  sd    /1DE((CD!14<|<=-)q	"!15R@rp   c                @    \        . RO4      pRp\        W#RVR7       R# )}Ô%ITrz  r  r
  N)r  rz  gu <7~)r   r
  r
  s   &&  rm   test_large_valuesTestGMean.test_large_values  s    '(!5R8rp   c                    . ROpRp\         P                  ! RR7      ;_uu_ 4        \        W#VR7       RRR4       R#   + '       g   i     R# ; i)rO   r   r}  r	  r  N)
rO   r  r  r  r  rD  rY  rH  r!  ry   )r   r  r
  r
  s   &&  rm   test_1d_with_0TestGMean.test_1d_with_0  s6    
 4[[X&&aR0 '&&&s	   >A	z;ignore:invalid value encountered in log:RuntimeWarning:daskc                    . ROp\         P                  p\         P                  ! RR7      ;_uu_ 4        \        W#VR7       RRR4       R#   + '       g   i     R# ; i)rO   r}  r~  r  N)
rO   r  r  r  r  rD  rY  rH  r!  rU   )r   rb   r  r
  r
  s   &&  rm   test_1d_negTestGMean.test_1d_neg  s:    
 5&&[[**aR0 +***s   AA	Tr
  r   c                    . ROp. ROpRp\         P                  ! W#R7      p\        V\        P                  ! V4      RR7       R# )rW   GZ*oG8@r
  r
  r  Nr  rE   rw   rz   r   r   )r[   r  r/   r   rY   r
  s   &&    rm   r
  TestGMean.test_weights_1d_list  s8     !
 kk!-RZZ0t<rp   c                    \         P                  ! . RO4      p\         P                  ! . RO4      pRp\        W$VRVR7       R# )rW   r  r
  r
  Nr  r  r
  r
  s   &&   rm   r
  TestGMean.test_weights_1d  s3     HH_%((?+!gDRHrp   c           	         \         P                  ! . RO4      p\         P                  P                  . RO. ROR7      pRp\         P                  p\        W$VR\         P                  VR7       R# )	rW   r  r  r
  r
  Nr  )rE   rw   rz   r   r   rw   )ry   ry   ry   ry   ry   rW   )r   r   rx  r
  r   r
  s   &&   rm   r
  &TestGMean.test_weights_masked_1d_array  sP     HH'(%%++07I+JUU!gD "

r	3rp   r   N)r   r   r   r   r   r   r   r
  r
  r
  r
  r
  r  r  r	  r   r
  r
  r%   r
  r   r   r   s   @rm   r
  r
  y  s     [[F--
?-A	A9
 [[F11 [[E11 ==	=I 3 3rp   r
  c            
         a  ] tR tRt o R tR tR tR t]P                  P                  R4      ]P                  P                  R4      R 4       4       tR	 t]P                  P                  R^
^.^2^<.^Z^d..R3]P                  ! ^
^.^2^<.^Z^d..4      R
3.4      R 4       t]P                  P                  R. RO. RO. RO.R3. RO. RO. RO.R
3.4      R 4       t]P                  P                  R. RO. RO. RO.R3. RO. RO. RO.R
3.4      R 4       tR t]! RRR7      R 4       t]R 4       t]P                  P                  R. RO4      R 4       tRtV tR# )	TestPMeani  c                x    \         P                  ! W,          4      V P                  ,          ^V,          ,          # r  )r   r^  r  rK  re  s   &&rm   pmean_referenceTestPMean.pmean_reference  s$    qtqvv%1--rp   c                    \         P                  ! W V,          ,          4      \         P                  ! V4      ,          ^V,          ,          # r  )r   r^  )rK  re  r
  s   &&&rm   wpmean_referenceTestPMean.wpmean_reference  s-    wA~&8AaC@@rp   c                   \         P                  ! \        R R7      ;_uu_ 4        \        P                  ! VP                  . RO4      VP                  ^ .4      4       RRR4       \         P                  ! \        R R7      ;_uu_ 4        \        P                  ! VP                  . RO4      VP                  ^ .4      4       RRR4       R#   + '       g   i     Lw; i  + '       g   i     R# ; i)zPower mean only defined forr   Nr  )r   r   r   r[   r
  rY   r  s   &&rm   test_bad_exponentTestPMean.test_bad_exponent  s    ]]:-JKKKK

9-rzz1#? L]]:-JKKKK

9-rzz1#? LK LKKKKs   9C
9C C	 C1	c                F   . RORr2\         P                  \        P                  ! V4      V4      p\	        W#WAR7       . RORr2\         P                  \        P                  ! V4      V4      p\	        W#WAR7       . RO^r2\        P
                  ! R4      p\	        W#WAR7       R# )rO   r  r  NrX  g      r  rZ  )r  r  r   r   r
  rH  rc   rd   rK  re  r  s   &&   rm   r
  TestPMean.test_1d  sx    8#1++BHHQK;!/8$1++BHHQK;!/Q1''9:!/rp   r  r  c                Z    \         P                  ! ^^ .4      Rr2Rp\        W#VRVR7       R# )rW   r   r
  NrU   )r   r   r
  r   s   &&   rm   r
  TestPMean.test_1d_with_zero  s+     xxA1!cb9rp   c           	         \         P                  ! . RO4      Rr2Rp\        P                  ! \        VR7      ;_uu_ 4        \        W#VP                  VR7       RRR4       R#   + '       g   i     R# ; i)rW   Gz?z!The power mean is only defined...r   r  Nr
  )r   r   r   rb  r   r
  rb   )rc   rd   rK  re  r  s   &&   rm   r
  %TestPMean.test_1d_with_negative_value  sG    xx
#T15\\.88aBFFr2 9888s    A##A4	r1   c                t    \         P                  \        P                  ! V4      V4      p\	        WWCR 7       R# )r  Nr  r  r   r   r
  )rc   rK  re  rd   r  s   &&&& rm   test_2d_axisnoneTestPMean.test_2d_axisnone  s(     ++BHHQK;!/rp   c                @   \        \        V^ ,          4      4       UUu. uF\  p\        P                  \        P
                  ! \        \        V4      4       Uu. uF  qQV,          V,          NK  	  up4      V4      NK^  	  ppp\        WV^ VR7       R# u upi u uppi )ry   r
  N)r  r   r  r  r   r   r
  )rc   rK  re  rd   r  r  r  s   &&&&   rm   r
  TestPMean.test_2d_axis0  s     3qt9%	
 & %%5Q=9=aA$q''=9:A &	 	 
 	!aB7	 :
s   :BB1BBc                    V Uu. uF-  p\         P                  \        P                  ! V4      V4      NK/  	  pp\	        WV^VR7       R# u upi )rW   r
  Nr(  )rc   rK  re  rd   a_r  s   &&&&  rm   r
  TestPMean.test_2d_axis1+  sC     IJJ"9,,RXXb\1=J!aB7 Ks   3Ac           	         . RORr2. ROp\         P                  \        P                  ! V4      W44      p\	        W#WTRVR7       R# )rE   r
  r
  Nr
  ރBr
  )r  r  r   r   r
  rc   rd   rK  re  r
  r  s   &&    rm   r
  TestPMean.test_weights_1d4  s6    ;1,,RXXa[!E!tKrp   Tr
  r   c                    . RORr2. ROp\         P                  \        P                  ! V4      W44      p\        P
                  ! W#VR7      p\        V\        P                  ! V4      RR7       R# )rE   r
  r
  r  Nr
  r1  r
  )r  r  r   r   r[   r
  r/   rY   )rc   rd   rK  re  r
  r  r   s   &&     rm   r
  TestPMean.test_weights_1d_list:  sQ    
 ;1,,RXXa[!E kk!0RZZ0t<rp   c           
        \         P                  ! . RO4      ^r2\         P                  P                  . RO. ROR7      p\         P                  ! W$R7      p\         P                  p\	        W#WTR\         P
                  VR7       R# )	rE   r  r
  r
  r
  Nr
  r
  r
  )r   r   rx  averager
  r   r2  s   &&    rm   r
  &TestPMean.test_weights_masked_1d_arrayH  sV    xx'1%%++n<+@**Q0UU!t "

r	3rp   Nc           
        a VR 8X  d   V3R lpM\        \        V4      p\        P                  ! ^^.^
^.^^..4      p\        P                  ! ^
^.^^.^^..4      pV! WaVR7      p\	        VSWVRVR7       R# )r  c                 2   < \         P                  V SV4      # r  )r  r  )rK  r?   r
  re  s   &&&rm   fun&TestPMean.test_weights_2d.<locals>.funY  s     11!Q@@rp   )r?   r
  r
  r
  N)rj  r[   r   r   r
  )	rc   r?   fun_namere  rd   r;  rK  r
  r  s	   &&&f&    rm   test_weights_2dTestPMean.test_weights_2dQ  s     ))A %*CHHq!fr1g1v./((RGaVaV45aG4!QG$SUVrp   r   r  ro  r
  r
  r
  r
  )r?   r=  re  ))Nr  g3E#@)ry   r  ry   )rW   r
  rU   )r   r   r   r   r  r  r  r
  r   r   r   r
  r
  r  r   r   r)  r
  r
  r
  r   r
  r%   r
  r>  r   r   r   s   @rm   r  r    s    .A@0 [[ VW[[ WX: Y X:
3 [[8b"XCy
)4	0
((RHr2hS	2
3S	9	;
0
0 [[-/B
CT	J,.A
BC	H	J
8
8 [[-/B
CT	J,.A
BC	H	J
8
8L ==	= 3 3 [[!		W	Wrp   r  c            	          a  ] tR tRt o ]P
                  ! ^4      ^,           P                  4       tRt]P                  ! ]R4      P                  4       t
R t]! RRR7      R 4       t]R 4       t]P"                  P%                  R	4      ]P"                  P%                  R
4      ]P"                  P'                  R^ R]P(                  ]P*                  34      R 4       4       4       tR tR tR tR tR tR tR tRtV tR# )TestGSTDic  gv aZ@c                    \         P                  ! VP                  V P                  4      4      p\	        W!P                  V P
                  4      4       R # r  )r[   r  rY   array_1dr/   gstd_array_1drc   rd   gstd_actuals   && rm   test_1d_arrayTestGSTD.test_1d_arrayj  s4    jjDMM!:;ZZ0B0B%CDrp   Tz$Only NumPy supports array-like inputr   c                    \         P                  ! \        V P                  4      4      p\	        W P
                  4       R # r  )r[   r  rQ
  rC  r
   rD  rE  s   && rm    test_1d_numeric_array_like_input)TestGSTD.test_1d_numeric_array_like_inputn  s'    jjt}}!56%7%78rp   c                    R p\         P                  ! \        \        3VR7      ;_uu_ 4        \        P
                  ! R4       RRR4       R#   + '       g   i     R# ; i)z.could not convert string to float|The DType...r   z*You cannot take the logarithm of a string.N)r   r   r   r&  r[   r  r
  s   && rm   #test_raises_error_non_numeric_input,TestGSTD.test_raises_error_non_numeric_inputs  s:    B]]J	2'BBJJCD CBBBs   AA	r  r  	bad_valuec                   VP                  V P                  V.,           4      p\        P                  ! V4      '       dX   \	        V4      '       gG   R p\
        P                  ! \        VR7      ;_uu_ 4        \        P                  ! V4      pRRR4       M\        P                  ! V4      p\        XVP                  \        P                  4      4       R#   + '       g   i     L;; i)z3The geometric standard deviation is only defined...r   N)rY   rC  r   r  r(   r   rb  r   r[   r  r0   rb   )rc   rO  rd   rf   r  r   s   &&&   rm   test_returns_nan_invalid_value'TestGSTD.test_returns_nan_invalid_valuey  s     JJt}}	{23;;y!!-*:*:KGnG<<jjm =< **Q-CRZZ/0	 =<s   7CC(	c                    VP                  . ROVP                  ^^^..4      p\        P                  ! V^R7      p\	        W1P                  ^\
        P                  .4      4       R# )rW   r>   N)rW   rW   rW   r-
  )rY   rb   r[   r  r/   r   )rc   rd   rK  rF  s   &&  rm   test_propagates_nan_values#TestGSTD.test_propagates_nan_values  sK    JJ1a'89:jj+ZZBFF%<=rp   c                    VP                  V P                  4      p\        P                  ! W"P                  ^ ,          R7      p\        W1P                  VP                  4      4       R# )ry   rM  N)rY   rC  r[   r  r  r0   rb   r   s   &&  rm   )test_ddof_equal_to_number_of_observations2TestGSTD.test_ddof_equal_to_number_of_observations  s?    JJt}}%jj,ZZ/0rp   c                    VP                  V P                  4      p\        P                  ! VR R7      pVP                  V P                  4      p\        W44       R # )Nr>   )rY   array_3dr[   r  rD  r/   rc   rd   rf   rF  r  s   &&   rm   test_3d_arrayTestGSTD.test_3d_array  s@    JJt}}%jj.jj++,)rp   c                    VP                  V P                  4      p\        P                  ! VRR7      pVP                  RR.4      p\	        W44       R# )rW   r>   g~d@g<
?Nr-  rY   rZ  r[   r  r/   r[  s   &&   rm   test_3d_array_axis_type_tuple&TestGSTD.test_3d_array_axis_type_tuple  s?    JJt}}%jj0jj*j12)rp   c                    VP                  V P                  4      p\        P                  ! V^ R7      pVP                  . RO. RO. RO.4      p\	        W44       R# )ry   r>   N)gĶ?@gQӫ@g֌@gן7R@)g%Ȁ@ge@gv6B5 @g _?)gE ?gީ?gk̊Y?g%:?r_  rc   rd   rf   rF  gstd_desireds   &&   rm   test_3d_array_axis_0TestGSTD.test_3d_array_axis_0  sJ    JJt}}%jj+zzOOO#
 
 	2rp   c                    VP                  V P                  4      p\        P                  ! V^R7      pVP                  . RO. RO.4      p\	        W44       R# )rW   r>   N)gN@g85@g'ĥ?gwth?)gHnaX?gG?gBu?gE?r_  rc  s   &&   rm   test_3d_array_axis_1TestGSTD.test_3d_array_axis_1  sG    JJt}}%jj+zzLL#
  	2rp   c                    VP                  V P                  4      p\        P                  ! V^R7      pVP                  . RO. RO.4      p\	        W44       R# )rE   r>   N)gt80?gі?g?)gۘ]~?gmT6(?g	G?r_  rc  s   &&   rm   test_3d_array_axis_2TestGSTD.test_3d_array_axis_2  sG    JJt}}%jj+zz??#
  	2rp   r   Nr  rU   ) r   r   r   r   r   r   r{   rC  rD  r]   rZ  rG  r   rJ  r%   rM  r   r   r   r  r!  rb   rQ  rT  rW  r\  r`  re  rh  rk  r   r   r   s   @rm   rA  rA  c  s     		)$q(002H"Mzz(I.557HE d+QR9 S9 E E
 [[ WX[[ VW[[[1b"&&"&&*AB1 C X Y1>
1
**333 3rp   rA  c            	         \         P                  ! \         P                  ! R R^4      \         P                  ! RR^4      \         P                  ! RR^4      34      p RpRp. ROp\        W4       F6  w  rE\	        \
        P                  ! W!V4      P                  V^RV 2R	7       K8  	  \	        \
        P                  ! ^2^dR 4      P                  R
^R7       R# )rD  r4  r  g?r'  ffffff?r  i  z
fail forp=)r  err_msggVݶ3;r  N)r   r   gs  gG|G{g	ɺM>6g>
ztt+g#ӌRM/gF׸fz2gU8u5g8M8gФ)Ba?g%վ?g*+a5?gś?gڒJ|>)r   rz  r5  r5  r	   r[   	binomtestr=  )ppr  rf   rr  re  r   s         rm   test_binomtestrr    s    	S#q1T43T435 
6B 	AA(G b"EOOA!4;;S(*j4D	F # C5<</$&(rp   c                  ,   R R .. RO. RO. RO. RO. RO. R	O. R
O. RO. RO.
p \        ^^4       F^  p\        V^,           4       Uu. uF$  p\        P                  ! W!R4      P                  NK&  	  pp\	        W0V^,
          ,          ^
R7       K`  	  R# u upi )r   r1   rW  N)r1   r   r1   )r  r   r   r  )r  r  r   r  r  )r        ?r   r   rt  r  )r        ?      ?r   rv  ru  r  )r  r        ?r   r   rw  r  r  )	      ?      ?     ?     @?r   r{  rz  ry  rx  )
      p?      ?      ?     @?r   r   r  r~  r}  r|  )      `?      ?      ?      ?      ?r   r  r  r  r  r  )r  r[   rp  r=  r   )r  r  r  r  s       rm   test_binomtest2r    s     
c
 +8G		*	E	D" 1b\;@Q<H<ac*11<HDqs)R8 Hs   *Bc                  ,   \        ^^4       U Uu. uFE  p \        ^^4       F2  p\        P                  ! W V,          RV,          4      P                  NK4  	  KG  	  pp p\	        V\
        P                  ! \        V4      \        4      4       \
        P                  ! . RNRNRNRNRNRNRNR	NR
NRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNR NR!NR"NR#NR$NR%NR&NR'NR(NR)NR*NR+NR,NR-NR.NR/NR0NR1NR2NR3NR4NR5NR6NR7NR8NR9NR:NR;NR<NR=NR>NR?NR@NRANRBNRCNRDNRENRFNRGNRHNRINRJNRKNRLNRMNRNNRONRPNRQNRRNRSNRTNRUNRVNRWNRXNRYNRZNR[N4      p\
        P                  ! . RNR\NR]NR^NR_NR`NRaNRbNRcNRNRdNReNRfNRgNRhNRiNRjNRkNRNRlNRmNRnNRoNRpNRqNRrNRsNRNRtNRuNRvNRwNRxNRyNRzNR{NR&NR|NR}NR~NRNRNRNRNRNR/NRNRNRNRNRNRNRNRNR8NRNRNRNRNRNRNRNRNRANRNRNRNRNRNRNRNRNRJNRNRNRNRNRNRNRNRNRSNRNRNRNRNRNRNRNRN4      p\        ^^4       U Uu. uFL  p \        ^^4       F9  p\        P                  ! V ^,           W,          RV,          4      P                  NK;  	  KN  	  pp p\        ^^4       U Uu. uFL  p \        ^^4       F9  p\        P                  ! V ^,
          W,          RV,          4      P                  NK;  	  KN  	  pp p\        WT^R7       \        Wc^R7       R# u upp i u upp i u upp i )rW   r   r1   grq?g     ?glq?gx0f#?g%d)MO?g   	o?g6?g:X@?r  gsw?g    ?gR'jMV?gEf?gF5a?gAQU?g'W?gk?rv  g
ņB?g  ?g$?g{dU'?gD:B?gwV?gR0Nf?gOq?r{  g[k^?g T+?gO?gggh(?gP-@?gOQ?g}^?gV7_i?r  ge$?gр?g#>?g5z@?g:?gf?gzP?g  ?g     ?gg*),?g}A_?g}aA?gH]@_?g
y7s?gPG?g>)\R?gjc6?gK?go; ,?g!O0?g?g}e?g5?g?!A^?gN/#?g*?g    @?g?g?g3?g.1?gdT\1-?gt0W59?goQC?gX4J?g   ?g
?gf?C"?g\6I?g4b?g|$or?gWNS~?gT?gXnc?g   \?gY\?gp ^a?gX-K?g#c?g
3?g75Q?gMJ[?gP8R?gw	%?g     ?gS g?gv^?g*uCi?g  a?g]?gE9Q?g/?g     ?g	x&~?g#?g5B?g	A'9?gpZ?gWV$u?gqIb?g  @N?g1Y?g5?gO?gc-?gk?g )?glMV?g?$?gT*r?gCqRv?grx?gωZ?gExY?g<T ?gJ9Ͻd?g `Ԗt?gT?gEz?gQ?g7C<*?g<?g~ K?g8?g~ȍEt?g⿒?g<v?gHE:?g8Z$?gbº5?gvC?g`Yw?gA?$??gE=?g4?g3?g{G9?gp?gH ?gz6f?g¯F?g(+?g	$V?gq^ws?g!?gXNJ?gK?g4P?g<q?gdV;?gy?g$w?gU<vO?gMX?g	șz*?giqSp?gMM?g0V$)?g]
yi/Q?gl?gl?g3Ȇ?gѾ_c?rW  N)r  r[   rp  r=  r   r   r  r   r!  r   r   )r  r  r  binom_testm1binom_testp1res4_p1res4_m1s          rm   test_binomtest3r    s    1b\9!5B<a OOAsBqD)00+7 1! 	 9rwws4y#./ 88 
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 L@ a<$1eArl qsACA.55.: 6$  < a<$1eArl qsACA.55.: 6$  < r:r:q9d<<s   AL/AL
ALc                   2   a  ] tR tRt o R tR tR tRtV tR# )TestTrimiF  c           
        \         P                  ! ^4      p\        \         P                  ! \        P
                  ! VR4      4      \         P                  ! ^
4      4       \        \         P                  ! \        P
                  ! VR4      4      \         P                  ! ^	4      4       \        \         P                  ! \        P
                  ! VRRR7      4      \         P                  ! ^^4      4       \        \         P                  ! \        P
                  ! VR	RR7      4      \         P                  ! ^^4      4       \        \        P
                  ! VR4      . 4       \        \        P
                  ! VRRR7      . 4       \        \        P
                  ! . R4      . 4       \        \        P
                  ! . R	RR7      . 4       \        \        P
                  ! . R
4      . 4       \         P                  ! ^4      P                  ^^4      p\         P                  ! ^^4      P                  ^^4      p^ p\        P
                  ! VRRVR7      p\        \         P                  ! WCR7      V4       ^p\        P
                  ! VP                  RRVR7      p\        \         P                  ! WCR7      VP                  4       R# )rP   rD  r4  left)tailr   )r  r?   r>   NtE]t?rH  )r   r   r   sortr[   trim1r]   r   )rc   rK  r  r?   trimmeds   &    rm   
test_trim1TestTrim.test_trim1H  s   IIbMRWWU[[C01299R=ARWWU[[C01299Q<@RWWU[[Cf=>YYq"%	'RWWU[[E?@YYq"%	'U[[C("-U[[Cf5r: 	U[[S)2.U[[U8"=U[[T*B/ IIbM!!!Q'ii2&&q!,++a6=RWWW0#6++acc3V$?RWWW0#%%8rp   c           
        \         P                  ! ^4      p\        \         P                  ! \        P
                  ! VR4      4      \         P                  ! ^^4      4       \        \         P                  ! \        P
                  ! VR4      4      \         P                  ! . RO4      4       \        \         P                  ! \        P
                  ! \         P                  ! ^4      P                  ^^4      R4      4      \         P                  ! ^^4      P                  ^^4      4       \        \         P                  ! \        P
                  ! \         P                  ! ^4      P                  ^^4      P                  R4      4      \         P                  ! . RO. RO.4      4       \        \        \        P
                  \         P                  ! ^4      P                  ^^4      P                  R	4       \        \        P
                  ! . R4      . 4       \        \        P
                  ! . R4      . 4       \        \        P
                  ! . R	4      . 4       R# )
rP   r4  rD  Nr  )rE   r   r   rw   rz   rJ   rF   rV  )rE   rF   rM   r  )r   rI   r  rL   rH  )r   r   r   r  r[   trimbothr   r]   r   r   r   )rc   rK  s   & rm   test_trimbothTestTrim.test_trimbothd  ss   IIbMRWWU^^Au56		!QHRWWU^^As34XX34	6RWWU^^BIIbM,A,A!Q,GMNYYq"%--a3	5RWWU^^BIIbM,A,A!Q,G,I,I,02 3XX~~>?	A 	j%..iim++Aq133T	; 	U^^B,b1U^^B.3U^^B-r2rp   c                N   \         P                  ! . RO4      p\         P                  ! . RO4      p\         P                  ! ^4      P                  ^^4      VR3,          p\         P                  ! ^4      P                  ^^RR7      VR3,          p\	        \
        P                  ! VR4      \         P                  ! . RO4      4       \	        \
        P                  ! VR4      \         P                  ! . RO4      4       \         P                  ! . RO4      p\         P                  ! ^4      P                  ^^4      VR3,          p\	        \
        P                  ! VR4      \         P                  ! . RO4      4       . ROp\	        \
        P                  ! VR4      R4       \	        \
        P                  ! . ROR4      R4       \         P                  P                  R4       \         P                  P                  ^RR7      pR FS  p\
        P                  ! VRVR7      p\
        P                  ! \         P                  ! W^ 4      R4      p	\	        W4       KU  	  \
        P                  ! VRR	R7      p\
        P                  ! VP                  4       R4      p	\	        W4       \        \        \
        P                  VR
4       \	        \
        P                  ! . R4      \         P                  4       \	        \
        P                  ! . R
4      \         P                  4       R	# )r   r   Fr  rt   rN   rg  r  r>   Nro  r   )r   rF   rE   ry   rI   rw   rO   rW   rJ   r   rz   )r   rw   ry   rW   rE   r   rV  )rt   r  g      -@g     4@r  )rW   ry   r   rE   )r   r   r  r  r  r  )rJ   rP   rQ   rL   r-
  rz   rh	  rW   rw   ry   r  rO   rg	  rI   r  r  r  r  rE   rM   r   rR   rF   r   )rw   r   r   rW   rE   ry   )rw   rz   r   rJ   )ry   rW   rE   r   rU   )r   r   r   r]   r   r[   	trim_meanr  r  randintr=  r  r   r   rb   )
rc   rK  idxr  r  idx4a4r?   r  r  s
   &         rm   test_trim_meanTestTrim.test_trim_meanv  s   HH78hh)*YYr]""1a(a0YYr]""1as"3CF;U__R.XX45	7U__R.XX23	5xx%YYr]""1a(q1U__R.XX;<	>%U__Q-t4U__]D93? 			tIIb|4$D??1d6D??2;;q#:DAD$ %
 q$T2qwwy$/T j%//1c: 	U__R-rvv6U__R-rvv6rp   r   N)	r   r   r   r   r  r  r  r   r   r   s   @rm   r  r  F  s     983$$7 $7rp   r  c                   >   a  ] tR tRt o R tR tR tR tR tRt	V t
R# )	TestSigmaClipi  c                D   \         P                  ! \         P                  ! R R^4      \         P                  ! ^ ^^4      34      p^p\        P                  ! V4      w  r4p\        VP                  4       V8  4       \        VP                  4       V8  4       \        WCP                  4       W#P                  4       ,          ,
          4       \        WSP                  4       W#P                  4       ,          ,           4       \        VP                  VP                  4       R# )r  rT   Nr   rz  r5  r[   	sigmaclipr   minmaxr   r^   r   r  rc   rK  factrj  r  upps   &     rm   test_sigmaclip1TestSigmaClip.test_sigmaclip1  s    NNBKKT26Ar18MNOooa(##S&&(T%%'\12S&&(T%%'\12QVVQVV$rp   c                ^   \         P                  ! \         P                  ! R R^4      \         P                  ! ^ ^^4      34      pRp\        P                  ! WV4      w  r4p\        VP                  4       V8  4       \        VP                  4       V8  4       \        WCP                  4       W#P                  4       ,          ,
          4       \        WSP                  4       W#P                  4       ,          ,           4       \        VP                  ^4       \        VP                  ^$4       R# )r  rT   r2   Nr  r  s   &     rm   test_sigmaclip2TestSigmaClip.test_sigmaclip2  s    NNBKKT26Ar18MNOooat4##S&&(T%%'\12S&&(T%%'\12QVVQQVVR rp   c                J   \         P                  ! \         P                  ! R R^4      \         P                  ! RR^4      34      pRp\        P                  ! WV4      w  r4p\        VP                  4       V8  4       \        VP                  4       V8  4       \        WCP                  4       W#P                  4       ,          ,
          4       \        WSP                  4       W#P                  4       ,          ,           4       \        V\         P                  ! R R^4      4       R# )r  rT   ?N)r   rz  r5  r[   r  r   r  r  r   r^   r   r  s   &     rm   test_sigmaclip3TestSigmaClip.test_sigmaclip3  s    NNBKKT26KKc157 8ooat4##S&&(T%%'\12S&&(T%%'\12QCr23rp   c                    \         P                  ! \         P                  ! R R^4      \         P                  ! RR^4      34      pRp\        P                  ! WV4      pRp\        W44       R# )r  rT   r  Nr  r  )clippedr  r  )r   rz  r5  r[   r  r   )rc   rK  r  r   r@  s   &    rm    test_sigmaclip_result_attributes.TestSigmaClip.test_sigmaclip_result_attributes  sV    NNBKKT26KKc157 8ooat,2
C,rp   c                    \         P                  ! ^
4      p\        \        P                  ! V4      ^ ,          V4       R# rO   N)r   r  r   r[   r  r  s   & rm   test_std_zeroTestSigmaClip.test_std_zero  s'    GGBKU__Q'*A.rp   r   N)r   r   r   r   r  r  r  r  r  r   r   r   s   @rm   r  r    s#     %	!	4-/ /rp   r  c                      a  ] tR tRt o R t]P                  P                  R^^.. 3^^.^3^^.^.3.4      R 4       tR t	R t
R tR tR	 tR
 tR tR tRtV tR# )TestAlexanderGoverni  c                   . RO. RO. RO. RO.pV Uu. uF)  p\         P                  ! V\         P                  R7      NK+  	  ppV Uu. uF)  p\         P                  ! V\         P                  R7      NK+  	  ppV Uu. uF)  p\         P                  ! V\         P                  R7      NK+  	  ppV Uu. uF)  p\         P                  ! V\         P
                  R7      NK+  	  pp\        P                  ! V!  p\        P                  ! V!  p\        P                  ! V!  p	\        P                  ! V!  p
VP                  VP                  u;8X  d%   V	P                  u;8X  d   V
P                  8X  g   Q h Q hVP                  VP                  u;8X  d%   V	P                  u;8X  d   V
P                  8X  g   Q h Q hR# u upi u upi u upi u upi )rR   r6   N)	rR   rR   rR   rR   rR   rR   rR   rQ   rQ   )	rM   rR   rQ   rQ   rQ   rQ   rQ   rP   rP   )	rM   rM   rR   rR   rR   rR   rR   rQ   rQ   )	r  rM   rR   rR   rR   rQ   rQ   rQ   rP   )
r   rY   r   r  r%  r   r[   alexandergovernr=  r>  )rc   r?  arg
args_int16
args_int32
args_uint8args_float64	res_int16	res_int32	res_uint8res_float64s   &          rm   test_compare_dtypes'TestAlexanderGovern.test_compare_dtypes  s   44446 BFF#bjjBHH5
FAEF#bjjBHH5
FAEF#bjjBHH5
FEIJTc

3bjj9TJ)):6	)):6	)):6	++\:  I$4$4 7  7$/$6$67 	8 7 	8 7##y':': =##='2'<'<= 	> = 	> = GFFJs   /F=/G=/G2/Gr  c                H   \         P                  ! \        \        R 7      ;_uu_ 4        \        P
                  ! V!  p\        VP                  \        P                  4       \        VP                  \        P                  4       RRR4       R#   + '       g   i     R# ; ir  )r   rb  r   r   r[   r  r   r>  r   rb   r=  r  s   && rm   test_too_small_inputs)TestAlexanderGovern.test_too_small_inputs  s[     \\,4IJJ''.C/RVV, KJJJr  c                z   \         P                  ! R R7      ;_uu_ 4        \        P                  ! ^^.\         P                  \         P                  .4      pRRR4       \        XP                  \         P                  4       \        VP                  \         P                  4       R#   + '       g   i     LZ; i)r}  r~  N)	r   r  r[   r  r!  r   r>  rb   r=  ry  s   & rm   test_bad_inputs#TestAlexanderGovern.test_bad_inputs  sf    [[**''A0@AC +S]]BFF+SZZ( +*s   8B**B:	c                   . RNRNRNRNRNRNRNRNRNRNRNRNRNRNR	NRNR NR
NRNRNRNRNRNR!NRNR"NR#NR$NR%NRNRNR&NRNR'NR(NR)NR*NR+NRNRNp. R,Op. R-Op\         P                  ! V4      \         P                  ! V4      \         P                  ! V4      r2p\        P                  ! WV4      p\	        VP
                  R4       \	        VP                  R4       R# ).a  
Data generated in R with
> set.seed(1)
> library("onewaytests")
> library("tibble")
> y <- c(rnorm(40, sd=10),
+        rnorm(30, sd=15),
+        rnorm(20, sd=20))
> x <- c(rep("one", times=40),
+        rep("two", times=30),
+        rep("eight", times=20))
> x <- factor(x)
> ag.test(y ~ x, tibble(y,x))

Alexander-Govern Test (alpha = 0.05)
-------------------------------------------------------------
data : y and x

statistic  : 1.359941
parameter  : 2
p.value    : 0.5066321

Result     : Difference is not statistically significant.
-------------------------------------------------------------
Example adapted from:
https://eval-serv2.metpsy.uni-jena.de/wiki-metheval-hp/index.php/R_FUN_Alexander-Govern

gb?g^s/@gQ\
@gIF@gpZ>q@g7D @g(Q<.@gON/@gs&@gzp"@gzl @g57@g>m@*a"@g,ZbI@gX9
]?g1@g;@gL97vp,+@g"@glA! &@go@gFQ?gsdlT6?Ng5gl"k gRh g-ѪZng	Ogҷ%6gw)ܿg789Ŀg3gg"Jbgy:@j-g2A gp/rgfT|7g^v+g٘Yg0/g)g!_5*gqTEgg1$@g	a, @gˤ$g9%gZ@gT6U'@gS g6aGn*@gO@g\\"g^4w@g0gr~5@gDP=@gٿԙg:4R/gOx]r!@gU4 gta)B@g,Gg2$@gD%?gI,VL&g@gч
;g5@gWJc@gYjK@@)gj7#@g<e,g}m(@gr2g#^9gr/P@g:RO!g'9?g6F
?gcʱ'gt*&gg~*0Ώ7@gWzx>gIK'@g?Ң@g7C5@g;C>ϯUg7@g)n}.^@r   rY   r[   r  r
   r>  r=  )rc   r  twoeightsolns   &    rm   test_compare_r"TestAlexanderGovern.test_compare_r  s   :"! "#5 "7I "!"#4"6H" ""3"5F" #" %6" 8I" #	" %8	" :L	"
 #"
 %9"
 ;L" !" #4" 6G" !" #4" 6H" !" #6" 8J" #" %7" 9J" !" #6" 8I" #" %8" :L" "" $7" 9K" !"	I7 **S/2::c?BJJu<M%$$Su5(=>%;<rp   c                   . R	Op. R
Op. ROp\         P                  ! V4      \         P                  ! V4      \         P                  ! V4      r2p\        P                  ! WV4      p\	        VP
                  RRR7       \	        VP                  RRR7        \	        VP
                  R4       \	        VP                  R4       R# )z
Data taken from 'The Modification and Evaluation of the
Alexander-Govern Test in Terms of Power' by Kingsley Ochuko, T.,
Abdullah, S., Binti Zain, Z., & Soaad Syed Yahaya, S. (2015).
g]FxK@r  rE  g R8߱?r  g.UikL@g&Zݱ?N)g{G&~@g(\E~@g=
ףp~@gfffff~@gp=
~@gףp=
k@gR@gQ2@g8@g`@g)\`@g=
ףp@g(\#@g@g=
ףpE@gQ@g
ףp=@gףp=
Մ@g33333#@)g=
ףpt@g{G&u@gq=
ףv@gQDy@g     X{@g\(P}@g]~@gt~@gzG~@g)\~@g1@gzG@)gGz8@g     @gp=
ב@g
ףp=@gGzԀ@gq=
ףր@gRi@g{Gt@gw@g=
ףp@gQS@gQ@g(\©@gQ-@gQ@r  )rc   youngmiddleoldr  s   &    rm   test_compare_scholar(TestAlexanderGovern.test_compare_scholar4  s    08GZZ.

60BBJJsOs$$UC8T:W48	: 	1Z0rp   c                R   . ROp. R	Op\         P                  ! V4      \         P                  ! V4      r!\        P                  ! W4      p\	        VP
                  RRR7       \	        VP                  RRR7        \	        VP
                  R4       \	        VP                  R4       R# )
a  
Data taken from 'Robustness And Comparative Power Of WelchAspin,
Alexander-Govern And Yuen Tests Under Non-Normality And Variance
Heteroscedasticity', by Ayed A. Almoied. 2017. Page 34-37.
https://digitalcommons.wayne.edu/cgi/viewcontent.cgi?article=2775&context=oa_dissertations
g[z4?r
  rE  gOZ}?g9$?g6MDd}?N)gQhgMOgY9gnSgdȿg}"Ogиp $?g8~4?g
p?gZ?g)J=?gX?gpG?gᛦ?gg?gh8en?g?guwg?gbX?g9SI?)gN]g	cZgAJigMg'gk,	Pg<gΈ׿g%zrKտg0BxҿgPNg:ǀgvꭁg?k~?gI\߇?gi?g<)?g0Xr?g
F%u?gsFZ*o?g7n:?r  )rc   r  r  r  s   &   rm   test_compare_scholar3)TestAlexanderGovern.test_compare_scholar3g  s|    "! BBB$$R,t<XD9	8 		2Y/rp   c                :   \         P                  ! . RO4      \         P                  ! ^\         P                  .4      3p\        P                  ! V!  p\        VP                  \         P                  4       \        VP                  \         P                  4       R# )rW   Nr  r   rY   rb   r[   r  r   r=  r>  )rc   r?  r   s   &  rm   test_nan_policy_propagate-TestAlexanderGovern.test_nan_policy_propagate  sZ    zz,'QK)@@##T*SZZ(S]]BFF+rp   c                   \         P                  ! . RO4      \         P                  ! ^\         P                  .4      3p\        \        RR7      ;_uu_ 4        \
        P                  ! VRR/  RRR4       R#   + '       g   i     R# ; i)rW   r   r   r   r   Nr  )r   rY   rb   r   r   r[   r  )rc   r?  s   & rm   test_nan_policy_raise)TestAlexanderGovern.test_nan_policy_raise  sW    zz,'QK)@@:-LMM!!4<G< NMMMs   A99B
	c                   \         P                  ! ^^^\         P                  ^.4      \         P                  ! ^\         P                  ^^.4      3p\         P                  ! . RO4      \         P                  ! . RO4      3p\        P                  ! VRR/ p\        P                  ! V!  p\        VP                  VP                  4       \        VP                  VP                  4       R# )rW   r   r   Nr  )rW   r  r  r  )rc   args_nanargs_no_nanres_nan
res_no_nans   &    rm   test_nan_policy_omit(TestAlexanderGovern.test_nan_policy_omit  s    ::q!Q23RZZBFFBPR@S5TTjj.

;0GG''EfE**K8
W^^Z%6%67W&&
(<(<=rp   c                   \         P                  ! . RO4      p\         P                  ! . RO4      p\        P                  ! \        RR7      ;_uu_ 4        \
        P                  ! W4      pRRR4       \        XP                  \         P                  4       \        VP                  \         P                  4       R#   + '       g   i     LZ; i)r]  r  r   Nr\  r^  )r   rY   r   rb  r   r[   r  r   r>  rb   r=  )rc   r  r  r   s   &   rm   rf  'TestAlexanderGovern.test_constant_input  sv    ZZ-.ZZ-.\\.0LMM''/C NS]]BFF+SZZ( NMs   B>>C	r   N)r   r   r   r   r  r   r   r  r  r  r  r  r  r  r  r  rf  r   r   r   s   @rm   r  r    s     >( [[Vq!fb\QFA;!Q!$NO- P-)B=H11f10f,=
>) )rp   r  c            	       2  a  ] tR tRt o R tR tR tR tR tR t	R t
R	 t]P                  P                  R
]P                   ! . RO4      ]P                   ! . RO4      ]P"                  ^ 33]P                   ! . RO4      ]P                   ! . RO4      ]P$                  ]P$                  33.4      R 4       t]P                  P                  R. RO4      R 4       tR tR tR tR t]P                  P                  RR. RO3.4      R 4       tR tR tRtV tR# )TestFOneWayi  c                p    \         P                  ! ^ ^.^ ^.4      w  r\        VR4       \        VR4       R# )ry   r   r   N)r[   f_onewayr   rc   r  re  s   &  rm   test_trivialTestFOneWay.test_trivial  s0    ~~q!fq!f-QQrp   c                    \         P                  ! ^ ^.^^.4      w  r\        VR4       \        V^\        P
                  ! R4      ,
          RR7       R# )ry   r   r1   ri  r  N)r[   r  r   r
   r   rH  r  s   &  rm   rX  TestFOneWay.test_basic  sA     ~~q!fq!f-Q1rwws|+%8rp   c                    . RO. R	O. R
O.p\         P                  ! VRR/ w  r#\        VRRR7       \        VRRR7       R# )(\5I@r  FgM;yQ?ri  r  gWe?Ng(\5IgHz'D@gףp=
2g
ףp=A@g333333g)\(?gq=
ףp7@rA   g333333.@gRQ#@gzG'@rp  g=
ףp#@gGz."@gp=
ף
@r[   r  r
   )rc   samplesr  re  s   &   rm   test_unequal_varTestFOneWay.test_unequal_var  sE    =+35 ~~w8%8& 	,59,59rp   c                    . RO. RO. RO.pRp\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! VRR/  RRR4       R#   + '       g   i     R# ; i)	r   z(Expected a boolean value for 'equal_var'r   r  FalseNr  r  r  )r   r   r&  r[   r  )rc   r  r  s   &  rm   test_equal_var_input_validation+TestFOneWay.test_equal_var_input_validation  sJ    =+35 =]]9G44NNG7w7 5444s   AA$	c                z    \         P                  ! ^.^.. RO4      w  r\        VRRR7       \        VRRR7       R# )rE   rD  r  Nr  ro  r  r  r  s   &  rm   test_known_exactTestFOneWay.test_known_exact  s4     ~~qcA3	23U+3U+rp   c                    \         P                  ! R R.\         P                  R7      p\         P                  ! RR.\         P                  R7      p\        P                  ! W4      w  r4\        VRRR7       R# )	    r6       gŸ?ri  r  N)r   r   uint16r[   r  r
   )rc   rK  rW  r  re  s   &    rm   test_large_integer_array$TestFOneWay.test_large_integer_array  sQ    HHc3Zryy1HHc3Zryy1~~a# 	.U;rp   c                    \         P                  ! R R.\         P                  R7      p\         P                  ! RR.\         P                  R7      p\        P                  ! W4      pRp\        W44       R# )r  r  r6   r  r  Nr  )r   r   r  r[   r  r   )rc   rK  rW  r   r@  s   &    rm   test_result_attributes"TestFOneWay.test_result_attributes  sM    HHc3Zryy1HHc3Zryy1nnQ",
C,rp   c                   . R
OpV EF  pRp\         P                  P                  \         P                  P                  \         P                  P	                  \
        4      RV4      4      p\        V4      ;_uu_ 4       pVP                  4       P                  R4      pRRR4       XR,           Uu. uF+  pVP                  4       '       g   K  VP                  4       NK-  	  pp\        P                  ! V^<R7      p	V	P                  w  rV
P                  \        4      p
\        P                  ! V
4      p\!        V^ ,          R,          4      pV Uu. uF  qW8H  ,          NK  	  pp\"        P$                  ! V!  pRpVV9   d   Rp\'        V^ ,          WSRV 2R	7       EK  	  R#   + '       g   i     EL; iu upi u upi )
SiRstv.datr  zdata/nist_anova
N:r  rQ  N)skiprowsr  zFailing testcase: )r  ro  )r  z
SmLs01.datz
SmLs02.datz
SmLs03.datzAtmWtAg.datz
SmLs04.datz
SmLs05.datz
SmLs06.dat
SmLs07.dat
SmLs08.dat
SmLs09.datrU   )r  r  r   )ospathabspathjoindirname__file__openreadsplitstripr   loadtxtr   r  r!  uniquer  r[   r  r
   )rc   	filenames	test_caser  fnamerA  contentline	certifieddatafrg   rf   catyr  xlistr   hard_tcs   &                rm   	test_nistTestFOneWay.test_nist  s^   ?	 #IDGGOOBGGLL1J1BI%O PEe&&(... 29%. *.$ JJL &.I *JJur2E77DAA99Q<Dil2&'A(,-1qvYYE-..%(C AGG#CFA&8$DF F- # * .s   ? F&2F:F:F?&F7za, b, expectedc                    R p\         P                  ! \        P                  VR7      ;_uu_ 4        \        P                  ! W4      w  rVV'       g
   Q Wc8H  4       h RRR4       R#   + '       g   i     R# ; i)%Each of the input arrays is constant;r   N)r   rb  r[   rc  r  )rc   rK  rW  r  r   rA  re  s   &&&&   rm   rf  TestFOneWay.test_constant_input"  sO     6\\%44C@@>>!'DA#am#1 A@@@s   *A&&A7	r?   c                   \         P                  ! . RO. RO. R	O. R
O. RO.4      p\         P                  ! . RO. RO. RO. RO. RO. RO. RO. RO.4      p\         P                  ! . RO. RO. RO. RO.4      pVR9   d(   VP                  pVP                  pVP                  p^ pM^pRp\        P                  ! \
        P                  VR7      ;_uu_ 4        \
        P                  ! W#WAR7      w  rxRRR4       R F  p	\
        P                  ! \         P                  ! W)V4      \         P                  ! W9V4      \         P                  ! WIV4      4      w  r\        XV	,          V
RR7       \        XV	,          VRR7       K  	  R F  p	\        P                  ! \
        P                  VR7      ;_uu_ 4        \
        P                  ! \         P                  ! W)V4      \         P                  ! W9V4      \         P                  ! WIV4      4      w  r\        XV	,          V
4       \        XV	,          V4       RRR4       K  	  R#   + '       g   i     EL^; i  + '       g   i     K  ; i)rW   r:  r   r>   Nri  r  )rW   r   r   r   )rE   rw   r   r   )r   rz   r   r   r$  )r   rW   rw   r   )r   rz   rw   r   )r   r   rw   r   )rW   rw   rw   r   )rw   rw   rw   r   )rE   r   rw   r   )rF   rE   rw   r   )rE   rE   rw   r   )r   r   r   r   )r   rE   r   r   )rw   r   r   r   rU   rW   rV  rW  )r   r   r   r   rb  r[   rc  r  taker
   r   )rc   r?   rK  rW  rj  	take_axisr@  rA  re  r  fjpjs   &&          rm   test_2d_inputsTestFOneWay.test_2d_inputs-  s   HHl""""	$ %
 HHl"""""""$ % HHl"""$ %
 7?AAAII:\\%44HEE>>!5DA F
 A^^BGGA)$<$&GGA)$<$&GGA)$<>FB AaD"51AaD"51  Ae88IIi(@(*i(@(*i(@B QqT2&QqT2& JI  FEE JIIs   I8B II	I+c           
        ^\         P                  ! R^4      P                  ^^^4      ,          p^\         P                  ! R^4      P                  ^^^4      ,          p\         P                  ! ^\         P                  ! R^q4      P                  ^^^4      ,          4      p\        P
                  ! WV^R7      w  rEVP                  R8X  g   Q hVP                  R8X  g   Q h\        VP                  ^ ,          4       F  p\        VP                  ^,          4       F^  p\        P
                  ! WRV3,          W&RV3,          W6RV3,          4      w  r\        WWg3,          4       \        WWg3,          4       K`  	  K  	  R# )rW   r   r>   r   N)r   rJ   )	r   r   r]   cosr[   r  r  r  r
   )
rc   rK  rW  rj  rA  re  r  r  fijpijs
   &         rm   test_3d_inputsTestFOneWay.test_3d_inputs]  s%   biiY'//1a88biiY'//1a88FF1RYYsI.66q!Q??@~~aAA.ww&   ww&   qwwqz"A1771:& >>!q!G*a1aj!q!G*MqtW-qtW- ' #rp   c                   \         P                  ! \        \        R 7      ;_uu_ 4        \        P
                  ! . RO. . RO4      p\        V\        P                  \        P                  34       RRR4       R#   + '       g   i     R# ; i)r   Nr  r  )	r   rb  r   r   r[   r  r   r   rb   r(  s   & rm   test_length0_1d_error!TestFOneWay.test_length0_1d_errorn  sN    \\,4IJJ^^Ir<@F"&&"&&!12 KJJJs   AA::B	c                   \         P                  ! \        \        R 7      ;_uu_ 4        ^p\        P
                  ! ^V34      p\        P
                  ! ^ V34      p\        P
                  ! ^V34      p\        P                  ! W#V4      w  rV\        P                  ! V3\        P                  R7      p\        WW4       \        Wg4       RRR4       R#   + '       g   i     R# ; i)r   r  N)r   rb  r   r   r   r  r[   r  r~   rb   r   )rc   ncolsrK  rW  rj  rA  re  r  s   &       rm   test_length0_2d_error!TestFOneWay.test_length0_2d_errort  s    \\,4IJJEE
#AE
#AE
#A>>!*DA77E87D!! KJJJs   B!CC%	c                   \         P                  ! \        4      ;_uu_ 4        \        P                  ! ^
.^.^.^.4      p\        V\        P                  \        P                  34       RRR4       R#   + '       g   i     R# ; ir  )r   rb  r   r[   r  r   r   rb   r(  s   & rm   test_all_length_oneTestFOneWay.test_all_length_one  sT    \\,--^^RD2$rd;F"&&"&&!12 .---s   AA55B	r?  c                    R p\        \        VR7      ;_uu_ 4        \        P                  ! V!   RRR4       R#   + '       g   i     R# ; i)z$At least two samples are required...r   N)r   r&  r[   r  )rc   r?  r  s   && rm   test_too_few_inputsTestFOneWay.test_too_few_inputs  s/    89G44NND! 5444s	   ;A	c                    \         P                  ! R4      p\         P                  ! R4      p\        \        4      ;_uu_ 4        \        P
                  ! W^R7       RRR4       R#   + '       g   i     R# ; ir   r>   Nr  )rw   r   )r   r  r   r$   r[   r  rc   rK  rW  s   &  rm   test_axis_errorTestFOneWay.test_axis_error  sD    GGFOGGFO9%%NN1a( &%%%   A''A8	c                    \         P                  ! R4      p\         P                  ! R4      p\        \        4      ;_uu_ 4        \        P
                  ! W^R7       RRR4       R#   + '       g   i     R# ; irX  )r   r  r   r   r[   r  rY  s   &  rm   test_bad_shapesTestFOneWay.test_bad_shapes  sD    GGFOGGFO:&&NN1a( '&&&r\  r   N)r  r  r  r
  )rZ  rU   ry   rW   r  )r   r   r   r   r  rX  r  r
  r  r  r  r7  r   r   r  r   r   r!  rb   rf  rB  rH  rK  rO  rR  rU  rZ  r^  r   r   r   s   @rm   r  r    s    9:88,<-F@ [[-	,	)!4rvvqkB	,	,!7"&&"&&9IJ0
 $	$ [[V^4-' 5-'^."3	"3
 [[Vb9,%78" 9"
)) )rp   r  c                   \   a  ] tR tRt o R tR tR tR tR tR t	R t
R	 tR
 tR tRtV tR# )TestKruskali  c                   ^.p^.p\         P                  ! W4      w  r4\        VR4       \        V\         P                  P
                  P                  V^4      4       \         P                  ! \        P                  ! V4      \        P                  ! V4      4      w  r4\        VR4       \        V\         P                  P
                  P                  V^4      4       R# )rW   r   N)	r[   kruskalr   r	   r  r}  r  r   r   rc   rf   rg   hre  s   &    rm   test_simpleTestKruskal.test_simple  s    CC}}Q"QAu2277::1a@A}}RXXa["((1+6QAu2277::1a@Arp   c                   . ROp. ROp\         P                  ! W4      w  r4\        VR^
R7       \        V\         P                  P                  P                  R^4      4       \         P                  ! \        P                  ! V4      \        P                  ! V4      4      w  r4\        VR^
R7       \        V\         P                  P                  P                  R^4      4       R# )rW   r  NrW   r   rw   rJ   rI   rE   r   rz   rF   rO   r  )r[   rc  r	   r  r}  r  r   r   rd  s   &    rm   rX  TestKruskal.test_basic  s    }}Q"Au"5Au2277::5!DE}}RXXa["((1+6Au"5Au2277::5!DErp   c                r    ^.p^^.pRpRpW4,          p\         P                  ! W4      w  rg\        We4       R# )rW   r  Nrt  )r[   rc  r   rc   rf   rg   h_uncorrr  r  re  re  s   &       rm   test_simple_tieTestKruskal.test_simple_tie  s=    CF*?}}Q" 	Q!rp   c                    . ROp. ROpRp^\        ^4      R,          ,
          pW4,          p\        P                  ! W4      w  rg\        We4       R# )rW   N)rW   rW   rW   rE   )rE   rE   rE   rE   r     )r  r[   rc  r	   rm  s   &       rm   test_another_tieTestKruskal.test_another_tie  sE    >5,-::?}}Q"A(rp   c                   . ROp. ROp^^.pRp^\        ^4      R,          ,
          pWE,          p\        P                  ! WV4      w  rx\        Wv4       \        V\        P                  P
                  P                  V^4      4       R# )rW   Nr  r>  r8   rr  )r  r[   rc  r	   r  r}  r  )	rc   rf   rg   r,  rn  r  r  re  re  s	   &        rm   test_three_groupsTestKruskal.test_three_groups  ss    FG5,-::?}}Q1%A(Au2277::1a@Arp   c           	     "   . ROp. ROp. p\         P                  ! \        \        R7      ;_uu_ 4        \	        \
        P                  ! WV4      \        P                  \        P                  34       RRR4       R#   + '       g   i     R# ; i)rW   r   Nr  r>  )	r   rb  r   r   r   r[   rc  r   rb   )rc   rf   rg   r,  s   &   rm   r  TestKruskal.test_empty  sV    \\,4IJJqQ/"&&"&&1AB KJJJs   A A==B	c                \    . ROp. ROp\         P                  ! W4      pRp\        W44       R# )rW   Nri  rj  r  )r[   rc  r   )rc   rf   rg   r   r@  s   &    rm   test_kruskal_result_attributes*TestKruskal.test_kruskal_result_attributes  s'    mmA!,
C,rp   c                   \         P                  ! R 4      p\         P                  V^	&   \        \        P
                  ! W4      \         P                  \         P                  34       \        \        P
                  ! WRR7      R4       \        \        \        P
                  WRR7       \        \        \        P
                  WRR7       R# )r   r   r   r   r   Nr   )	r   r   rb   r   r[   rc  r   r   r   r  s   & rm   r  TestKruskal.test_nan_policy  su    IIcNvv!U]]1(266266*:;EMM!6BJOj%--'Jj%--(Krp   c                    R p\         P                  P                  V4      p\         P                  P                  V4      ^2,           p\        P                  ! W#4      w  rE^ p\        WV4       R# )rP
  N)r   r  r  r[   rc  r	   )rc   r  rf   rg   re  re  r  s   &      rm   test_large_no_samples!TestKruskal.test_large_no_samples  sM    IIOOAIIOOA#}}Q"A(rp   c                    R p\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! 4        RRR4       R#   + '       g   i     R# ; i)z-Need at least two groups in stats.kruskal\(\)r   N)r   r   r   r[   rc  r;  s   & rm   test_no_args_gh20661 TestKruskal.test_no_args_gh20661  s0    B]]:W55MMO 6555s   AA	r   N)r   r   r   r   rf  rX  ro  rs  rv  r  r{  r  r  r  r   r   r   s   @rm   ra  ra    sA     BF	")
BC-L) rp   ra  c                     a  ] tR tRt o ]P
                  P                  R. RO4      R 4       t]P
                  P                  R. RORR3. RORR3.4      R	 4       t. ROt	]P
                  P                  R
. RO4      ]P
                  P                  R]	4      R 4       4       t
]P
                  P                  R]	4      R 4       t]P
                  P                  R]	4      ]P
                  P                  R^ ^.4      R 4       4       tRtV tR# )TestCombinePvaluesi  z+method, expected_statistic, expected_pvaluev!:@/?c                    . ROp\         P                  ! VP                  V4      VR7      p\        VP                  VP                  V4      4       \        VP
                  VP                  V4      4       R# r  r  Nr  r4  rG  )r[   combine_pvaluesrY   r/   r>  r=  )rc   rd   r  r  r  rf   r   s   &&&&&  rm   test_reference_values(TestCombinePvalues.test_reference_values  sR     ##BJJqM&Arzz2D'EF

BJJ$?@rp   z,weights, expected_statistic, expected_pvaluega;?grmT?c                   VP                  . RO4      p\        P                  ! VRVP                  V4      R7      p\        VP                  VP                  V4      4       \        VP
                  VP                  V4      4       R# )r  stouffer)r  r
  Nr  )rY   r[   r  r/   r>  r=  )rc   rd   r
  r  r  rf   r   s   &&&&&  rm   test_weighted_stouffer)TestCombinePvalues.test_weighted_stouffer   s^     JJ}%##Aj"**WBUVrzz2D'EF

BJJ$?@rp   rm  r  c                P   ^
^rT\         P                  P                  R4      pVR8X  dp   VP                  VP	                  VP                  V4      4      WE34      pVP                  VP                  VP                  RRV4      R4      VR,          .^R7      pMrVR8X  d0   VP                  VP                  RRV4      WT34      P                  pM<VR	8X  d6   VP                  VP	                  VP                  ^ ^WE3R
7      4      ^ R7      pTP	                  \        XP                  ^ ,          4       Uu. uF3  p\        \        P                  ! WxR3,          VR7      ^,          4      NK5  	  up4      p	VP!                  V	R,          V	RR ,
          ^ 8  4      '       g   Q hR# u upi )rO   l	   TrU(	"b-= singlerD  rF  r   r  r>   r  r  r  r  NrU   r=  )r   r  )r   r  r  r  rY   r  r]   r5  r   r  r  r  r  r  r[   r  r  )
rc   rm  r  rd   r  r  r  pvaluessr  combined_pvaluess
   &&&&      rm   test_monotonicity$TestCombinePvalues.test_monotonicity   st    11ii##$KL hrzz#**Q-'@1&IHyy"**R[[c1-Ew"O"*5/"39: ! <Hr{{3Q'?!HJJH wwrzz#++a!+*HIPQwRH::8>>!,-'
- %''AvFqIJ-'
  vv&r*-=cr-BBaGHHHH	'
s   49F#c                    \         P                  ! VP                  . RO4      VR7      p\        VP                  V^ ,          4       \        VP
                  V^,          4       R# r  )r[   r  rY   r0   r>  r=  )rc   r  rd   r   s   &&& rm   rQ  TestCombinePvalues.test_result7   sA    ##BJJ}$=fMs1v.

CF+rp   r?   c                   \         P                  P                  R 4      pVP                  VP                  RR7      4      pV^ 8X  d   VP                  MTp\
        P                  ! WRVR7      pVfl   VP                  VR4      p\
        P                  ! WQR7      p\        VP                  VP                  4       \        VP                  VP                  4       R# V^ 8X  d   VP                  MTpVR,          VR,          r\
        P                  ! WR7      p
\
        P                  ! WR7      p\        VP                  ^ ,          V
P                  4       \        VP                  ^,          VP                  4       \        VP                  ^ ,          V
P                  4       \        VP                  ^,          VP                  4       R# )	l   2'$FV r  )r?   r  Nr  rE   rO   r  rq  rr  )r   r  r  rY   r   r[   r  r]   r/   r>  r=  )rc   r  r?   rd   r  rf   r   r  r  r  ref0ref1s   &&&&        rm   r  TestCombinePvalues.test_axis=   s:   
 ii##O4JJszzwz/0AIACCA##A@<

1e$A''9CCMM3==9CJJ

3AIACCA4!D'B$$R7$$R7a($..9a($..9

1t{{3

1t{{3rp   r   N))r  g'"x-@g({#H?)r  r  r  )r  gQ4gF?)tippettr  gL^i?)mudholkar_georgegzP@guKqN?r   r   r   )r   r   r   )r  r  r  r  r  )r  r  r  )r   r   r   r   r   r   r  r  r  r  r  rQ  r  r   r   r   s   @rm   r  r    s0     [[5	GHAHA [[ 	7
)+>	?
)+=	>	@	AA	AA OG[[Y(CD[[Xw/I 0 EI0 [[Xw/, 0,
 [[Xw/ [[VaV,4 - 04rp   r  c                   B   a  ] tR tRt o RtR tR tR tR tR t	Rt
V tR	# )
TestCdfDistanceValidationiY   z[
Test that _cdf_distance() (via wasserstein_distance()) raises ValueErrors
for bad inputs.
c           	         \        \        \        P                  ^.^.^.^^.4       \        \        \        P                  ^.^.^^ .4       R# r	  r   r   r[   wasserstein_distancer|  s   &rm   &test_distinct_value_and_weight_lengths@TestCdfDistanceValidation.test_distinct_value_and_weight_lengths_   sG     	j%"<"<cA3aV	-j%"<"<qcA3AOrp   c                    \        \        \        P                  ^ ^.^.^ ^ .4       \        \        \        P                  ^ ^.^.^^.^ .4       R# )ry   Nr  r|  s   &rm   test_zero_weight*TestCdfDistanceValidation.test_zero_weightf   sN     	j%"<"<!fqcAq6	+j%"<"<!fqcAq6A3	0rp   c           	     Z    \        \        \        P                  ^ ^.^^.^^.^R.4       R# )ry   NrU   r  r|  s   &rm   test_negative_weights/TestCdfDistanceValidation.test_negative_weightsn   s-    j%"<"<!fq!fq!fq"g	7rp   c                    \        \        \        P                  . ^^.4       \        \        \        P                  ^.. 4       R# r  r  r|  s   &rm   test_empty_distribution1TestCdfDistanceValidation.test_empty_distributions   s2     	j%"<"<b1a&Ij%"<"<qc2Frp   c           	     x    \        \        \        P                  . RO^^.^\        P
                  ^.^^.4       R# r{  )r   r   r[   r  r   r!  r|  s   &rm   test_inf_weight)TestCdfDistanceValidation.test_inf_weighty   s0    j%"<"<!Q!RVVQ!Q	Arp   r   N)r   r   r   r   r5  r  r  r  r  r  r   r   r   s   @rm   r  r  Y   s,     
P07
GA Arp   r  c                     a  ] tR tRt o RtR t]P                  P                  RR4      ]P                  P                  RR4      ]P                  P                  RR4      R 4       4       4       t	]P                  P                  RR4      ]P                  P                  R	R4      ]P                  P                  RR4      R
 4       4       4       t
]P                  P                  RR4      ]P                  P                  R	R4      ]P                  P                  RR4      R 4       4       4       tR t]P                  P                  RR4      ]P                  P                  R	R4      ]P                  P                  RR4      R 4       4       4       t]P                  P                  RR4      ]P                  P                  R	R4      ]P                  P                  RR 4      R 4       4       4       tR t]P                  P                  R. R!O4      ]P                  P                  R. R!O4      R 4       4       tRtV tR# )"TestWassersteinDistanceNDi   z7Tests for wasserstein_distance_nd() output values.
    c                &   . ROp. ROp\         P                  ! W4      p\        P                  ! . RO4      p\        P                  ! . RO4      p\        P                  ! WE,          4      \        P                  ! V4      ,          p\        W64       R# )rW   N)r  r  r  r  r  r  r  r  r  r  )r   rE   rz   rW   r  )r  r  r:  r:  r:  r	  r	  r	  r	  r	  r	  r	  )rJ   rW   )r   r   r8   r   r   r   )r   gw@r   ra  r   r   )r[   wasserstein_distance_ndr   r   r^  r
   )rc   r  r  r   flowdistr  s   &      rm   test_published_values/TestWassersteinDistanceND.test_published_values   sg    
"" ++A1 xx01xx@AffT[!"&&,.!rp   n_valuer  max_repeatsc                F   \         P                  P                  R 4      pVP                  ^W2\        R7      pVP                  W!3R7      p\         P
                  ! We^ R7      pVP                  \         P                  ! V4      4      p\         P
                  ! \         P                  ! \        V4      4      V4      p	\         P                  ! WR7      p
VP                  \        V4      4      pW{,          W,          r\        P                  ! WgW4      p\        V^ RR7       R# )l   na{F.aP	 )r  r7   r  r>   r
  rD  rE  N)r   r  r  rX	  r!  r  r^  r   r   bincountr  r[   r  r
   )rc   r  r  r  r  repeatsu_valuesv_values	v_weightsrange_repeat	u_weightsr	  r   s   &&&&         rm   test_same_distribution_nD3TestWassersteinDistanceND.test_same_distribution_nD   s     ii##$<=,,q+3,G::G?:399XQ7JJrvvg/	yy3w<!8'BKK@	I/&oy/?)++H	UQU+rp   nunvc                   \         P                  P                  R 4      pVP                  W3R7      p\         P                  ! W#34      pVP                  VR7      pVP                  VR7      p\         P                  ! \         P
                  P                  V^R7      VR7      p	\        P                  ! WVWx4      p
\        W4       R# )   }&=:! r  r>   r
  N)
r   r  r  rY  r7  r&  rX  r[   r  r
   )rc   r  r  r  r  r  r  r  r  r  r   s   &&&&       rm   test_collapse_nD*TestWassersteinDistanceND.test_collapse_nD   s     ii##$89::B::.88RJ'JJBJ'	JJBJ'	jjq99M++H	U!rp   c                (   \         P                  P                  R 4      pVP                  W3R7      pVP                  W#3R7      pVP                  VR7      pVP                  VR7      p\        P                  ! WVWx4      p	VP                  ^ V^R7      w  rVP                  W3R7      p\         P                  ! WZV^ R7      p\         P                  ! Wz\         P                  ! V4      ^ R7      p\        P                  ! WVWx4      p\        W4       R# )r  r  r>   N)	r   r  r  r[   r  rX	  insertrY  r
   )rc   r  r  r  r  r  r  r  r  r  add_rownrows	add_valuer   s   &&&&          rm   test_zero_weight_nD-TestWassersteinDistanceND.test_zero_weight_nD   s    
 ii##$89::B::.::B::.JJBJ'	JJBJ'	++H	Ua!4JJUMJ2	99X	BIIi"((5/J	++H	U!rp   c                   ^^.^^..\         P                  \         P                  ) ..^^.r2p\        P                  ! WV4      p\	        V\         P                  4       \         P
                  ! RR7      ;_uu_ 4        \         P                  \         P                  ..\         P                  \         P                  ) ..r!\        P                  ! W4      p\	        V\         P                  4       RRR4       R#   + '       g   i     R# ; i)rW   r}  r~  N)r   r!  r[   r  r   r  rb   )rc   uvvvuwdistances   &    rm   test_inf_values)TestWassersteinDistanceND.test_inf_values   s     !fq!f%"&&(9':QF00<Xrvv&[[**vvrvv&'266BFF7*;)<44R<H266* +***s   >A3C;;D	c                   \         P                  P                  R 4      pVP                  W3R7      pVP                  W#3R7      pVP                  VR7      pVP                  VR7      p\        P                  ! WVWx4      p	VP                  ^ V4      p
VP                  4       p\         P                  ! WZV^R7      p\         P                  ! WjV^R7      p\        P                  ! WVWx4      p\        W4       R# )l   Lq/ r  r>   N)r   r  r  r[   r  rX	  r  r
   )rc   r  r  r  r  r  r  r  r  r  add_dimr  r   s   &&&&         rm   test_multi_dim_nD+TestWassersteinDistanceND.test_multi_dim_nD   s    
 ii##$78::B::.::B::.JJBJ'	JJBJ'	++H	U,,q$'JJL	99X	B99X	B++H	U!rp   c                   \         P                  P                  R 4      pVP                  W3R7      pVP                  W#3R7      pVP                  VR7      pVP                  VR7      p\        P                  ! WVWx4      p	\        P
                  ! V4      p
V
P                  VR7      pVP                  VR7      p\        P                  ! W[,          V,           Wk,          V,           Wx4      p\        W4       R# )l   uAh~r  r  N)r   r  r  r[   r  ortho_groupr  r
   )rc   r  r  r  r  r  r  r  r  r  r  	transformshiftr   s   &&&&          rm   test_orthogonal_nD,TestWassersteinDistanceND.test_orthogonal_nD   s     ii##N3::B::.::B::.JJBJ'	JJBJ'	++H	U  &HH#H.	


%++H,@5,H)1)=)E)2? 	!rp   c                "   \         P                  P                  R 4      p\        P                  ! \
        RR7      ;_uu_ 4        VP                  RR7      pVP                  RR7      p\        P                  ! W#4      pRRR4       \        P                  ! \
        RR7      ;_uu_ 4        VP                  R	R7      pVP                  R
R7      p\        P                  ! W#4      pRRR4       \        P                  ! \
        RR7      ;_uu_ 4        VP                  RR7      pVP                  RR7      p\        P                  ! W#4      pRRR4       R#   + '       g   i     L; i  + '       g   i     L; i  + '       g   i     R# ; i)l   e36^[Y{lz Invalid input values. The inputsr   r  Nz Invalid input values. Dimensionsz(Invalid input values. If two-dimensional)r   rO   r  )rz   rE   rJ   )r  )r   r  r  r;  )r   r  r  r   r   r   r[   r  )rc   r  r  r  r  s   &    rm   test_error_code)TestWassersteinDistanceND.test_error_code!  s   ii##$>?]]:-OPPzz{z3Hzzyz1H--hAA Q ]]:-OPPzzuz-Hzzwz/H--hAA Q ]]:<> >zzwz/Hzzvz.H--hAA	> > QP QP> > >s$   ;E+;E*;E=E'	*E:	=F	u_sizev_sizec                   \         P                  P                  R 4      pVP                  V^3R7      pVP                  V^3R7      pVP                  4       pVP                  4       p\        P
                  ! Wg4      p\        P                  ! WE4      p	\        P                  ! Wg4      p
\        W4       \        W4       VP                  VR7      pVP                  VR7      p\        P
                  ! WgW4      p\        P                  ! WEW4      p	\        P                  ! WgW4      p
\        W4       \        W4       R# )l   Ku@* r  N)r   r  r  r  r[   r  r  r
   )rc   r  r  r  r  r  u_values_flatv_values_flatd1d2d3r  r  s   &&&          rm   test_optimization_vs_analytical9TestWassersteinDistanceND.test_optimization_vs_analytical!  s	    ii##K0::FA;:/::FA;:/ ( ( ''E**8>**=HJJFJ+	JJFJ+	''(1>**8(1>**=(1>rp   r   N)r   r  ru  )r   r   rJ   )rw   rO   )rF   rI   &   )rF   rQ   rg	  )r   rw   r  )rF   r-
  r  )rW   rE   rz   )rO   r  r  )rW   r   rw   )rJ   rR   r  )rE   r   rJ   )rW   rO   r  )r   r   r   r   r5  r  r   r   r  r  r  r  r  r  r  r  r  r   r   r   s   @rm   r  r     s    "& [[Y4[[VY/[[]G4, 5 0 5," [[T:.[[T;/[[VZ0" 1 0 /" [[T;/[[T;/[[VY/" 0 0 0" 	+ [[T<0[[T<0[[VY/" 0 1 1"" [[T;/[[T;/[[VY/" 0 0 0"$B  [[X{3[[X{3  4 4 rp   r  c                   N   a  ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
tV tR# )TestWassersteinDistancei.!  z4Tests for wasserstein_distance() output values.
    c                F   \        \        P                  ! ^ ^.^ .^^.^.4      R4       \        \        P                  ! ^ ^.^ .^^.^.4      R4       \        \        P                  ! ^ ^.^ .^^.^.4      ^4       \        \        P                  ! . RO. RO4      ^4       R# )ry   r1   r  Nr  r  r
   r[   r  r|  s   &rm   rf  #TestWassersteinDistance.test_simple2!  s     	&&1vsQFQC@	 	22FQC!Q!&	 	22FQC!Q!&	 	22y"	rp   c           	         \        \        P                  ! . RO. RO4      ^ 4       \        \        P                  ! . RO^^.. RO^^.4      ^ 4       R# rW   Nr  rx  )rW   rW   rW   r   rQ  )r   r[   r  r|  s   &rm   test_same_distribution.TestWassersteinDistance.test_same_distributionB!  sE     	U//	9EqI&&|aV'3aV=	rp   c           	     2   \        \        P                  ! ^ .^.4      ^4       \        \        P                  ! R.^.4      ^
4       \        \        P                  ! . RO. RO4      ^
4       \        \        P                  ! . RO. RO. RO. R	O4      R4       R# )
ry   rt   Nr  r  )rP   rQ   rR   rM   r  )rA   g@r
  )r
  rJ   r  )r   rW   rW   )rW   r   rW   r  r|  s   &rm   
test_shift"TestWassersteinDistance.test_shiftK!  sz     	22A3<a@22B4!=rB&&8LM	 	&&'0)=	rp   c           
         \        \        P                  ! . RO. RO. RO. RO4      \        P                  ! . RO. RO. RO. RO4      4       R# ry   N)ry   ry   rW   rW   rW   rW   rw   )ry   r   r   r   r   r   r   )rW   rW   rW   rW   rW   rW   rW   )rw   ry   rW   )ry   r   r   rW   rE   r   r  r|  s   &rm   test_combine_weights,TestWassersteinDistance.test_combine_weightsX!  s?     	&&%'<%'<> &&y)'0)=		>rp   c                   \         P                  ! R^R4      p\         P                  ! V4      p\        \        P
                  ! W4      \         P                  ! \         P                  ! V4      4      4       \         P                  ! \        V4      4      pVRRR1,          p\        \        P
                  ! WW44      \         P                  ! \         P                  ! V4      VR7      4       R# )rO   rG  Nr
  r  rU   )
r   r   r  r
   r[   r  r^   r  r   r7  )rc   r  r  r  r  s   &    rm   test_collapse%TestWassersteinDistance.test_collapseb!  s     IIc2s#MM!&&q,GGBFF1I	  IIc!f%	ddO	&&qYBJJrvvay)4	6rp   c           
         \        \        P                  ! . RO^^.. RO^^.4      \        P                  ! ^^.^^.^^.^^.4      4       R# rW   N)rW   rE   r^  r	  r  r|  s   &rm   r  (TestWassersteinDistance.test_zero_weightr!  sN    &&~1v'01a&:&&1v1v1v1vF	Hrp   c           	        \        \        P                  ! ^^\        P                  .^^.4      \        P                  4       \        \        P                  ! ^^\        P                  .\        P                  ) ^.4      \        P                  4       \        \        P                  ! ^\        P                  ) \        P                  .^^.4      \        P                  4       \        4       ;_uu_ 4       pVP                  \        R4       \        \        P                  ! ^^\        P                  .\        P                  ^.4      \        P                  4       RRR4       R#   + '       g   i     R# ; irW   r   N)	r   r[   r  r   r!  r   r   r   rb   rc   r   s   & rm   r  'TestWassersteinDistance.test_inf_valuesy!  s     	&&1bff~1v>FF	 	&&1bff~|DFF	 	&&BFF7BFF';aVDFF	   CJJ~'78**Aq"&&>BFFA;G !      7A'E((E9	r   N)r   r   r   r   r5  rf  r  r  r  r	  r  r  r   r   r   s   @rm   r  r  .!  s3      >6 H rp   r  c                   H   a  ] tR tRt o RtR tR tR tR tR t	R t
R	tV tR
# )TestEnergyDistancei!  z/Tests for energy_distance() output values.
    c                   \        \        P                  ! ^ ^.^ .^^.^.4      \        P                  ! ^4      R,          4       \        \        P                  ! ^ ^.^ .^^.^.4      \        P                  ! ^4      R,          4       \        \        P                  ! ^ ^.^ .^^.^.4      R4       \        \        P                  ! . RO. RO4      \        P                  ! ^4      R,          4       R# )ry   r1   r  r   Nr  r  r`  r   r[   energy_distancer   rH  r|  s   &rm   rf  TestEnergyDistance.test_simple!  s     	!!1a&1#1vs;GGAJO	 	E11FQC!Q!&GGAJ	 	E11FQC!Q!&	 	!!)Y7GGAJ**	,rp   c           	         \        \        P                  ! . RO. RO4      ^ 4       \        \        P                  ! . RO^^.. RO^^.4      ^ 4       R# r  )r   r[   r  r|  s   &rm   r  )TestEnergyDistance.test_same_distribution!  sB     	U**9i@!D!!,Aq!fM	rp   c                    \        \        P                  ! ^ .^.4      \        P                  ! ^4      4       \        \        P                  ! R.^.4      \        P                  ! ^4      R,          4       R# )ry   Nr  gS[:XL	@r  r|  s   &rm   r  TestEnergyDistance.test_shift!  sS     	E111#s;RWWQZH!!2$,GGAJ	!rp   c           
         \        \        P                  ! . RO. RO. RO. RO4      \        P                  ! . RO. RO. RO. RO4      4       R# r  r   r[   r  r|  s   &rm   r  'TestEnergyDistance.test_combine_weights!  s<     	!!"79N"79NP!!)Y	9M	Orp   c           
         \        \        P                  ! . RO^^.. RO^^.4      \        P                  ! ^^.^^.^^.^^.4      4       R# r  r  r|  s   &rm   r  #TestEnergyDistance.test_zero_weight!  sK    !!.1a&)aVL!!1a&1a&1a&1a&A	Crp   c           	        \        \        P                  ! ^^\        P                  .^^.4      \        P                  4       \        \        P                  ! ^^\        P                  .\        P                  ) ^.4      \        P                  4       \        \        P                  ! ^\        P                  ) \        P                  .^^.4      \        P                  4       \        4       ;_uu_ 4       pVP                  \        R4       \        \        P                  ! ^^\        P                  .\        P                  ^.4      \        P                  4       RRR4       R#   + '       g   i     R# ; ir  )	r   r[   r  r   r!  r   r   r   rb   r  s   & rm   r  "TestEnergyDistance.test_inf_values!  s     	U**Aq"&&>Aq6BBFFK!!1a.BFF7A,?FF	 	!!1rvvgrvv"6A?FF	   CJJ~'78%%q!RVVnrvvqkB !   r  r   N)r   r   r   r   r5  rf  r  r  r  r  r  r   r   r   s   @rm   r  r  !  s/     , !OC rp   r  c            	          a  ] tR tRt o . ROt. ROt^tR tR tR t	R t
R tR t]P                  P                  RR	. /R
. /R
. R	. /.4      R 4       tR tR tR tR tR tRtV tR# )TestBrunnerMunzeli!  c                   \         P                  ! V P                  V P                  R R7      w  r\         P                  ! V P                  V P                  RR7      w  r4\         P                  ! V P                  V P                  RR7      w  rV\         P                  ! V P                  V P                  R R7      w  rx\	        W$V P
                  R7       \	        WhV P
                  R7       \        W&8g  4       \	        VRV P
                  R7       \	        VRV P
                  R7       \	        VRV P
                  R7       \	        VRV P
                  R7       \	        VRV P
                  R7       \	        VRV P
                  R7       R# )	r  r  r  r  |	&	@gҏGg?g@-pL?N|	&	)r[   brunnermunzelrZ   rh
  r	   r  r   ri
  s	   &        rm   test_brunnermunzel_one_sided.TestBrunnerMunzel.test_brunnermunzel_one_sided!  s(   $$TVVTVVH$$TVVTVVK$$TVVTVVK$$TVVTVVHB0@0@AB0@0@AB 2(,(8(8	:B 3(,(8(8	:B 2(,(8(8	:B 3(,(8(8	:B 5(,(8(8	:B 3(,(8(8	:rp   c                   \         P                  ! V P                  V P                  R R7      w  r\         P                  ! V P                  V P                  R R7      w  r4\	        W$V P
                  R7       \	        VRV P
                  R7       \	        VRV P
                  R7       \	        VRV P
                  R7       R# )r  r  r  r'   ҏGw?Nr(  r[   r)  rZ   rh
  r	   r  rs
  s   &    rm   test_brunnermunzel_two_sided.TestBrunnerMunzel.test_brunnermunzel_two_sided!  s    $$TVVTVVM$$TVVTVVMB0@0@AB 2(,(8(8	:B 3(,(8(8	:B 5(,(8(8	:rp   c                x   \         P                  ! V P                  V P                  4      w  r\         P                  ! V P                  V P                  4      w  r4\	        W$V P
                  R 7       \	        VRV P
                  R 7       \	        VRV P
                  R 7       \	        VRV P
                  R 7       R# )r  r'  r-  Nr(  r.  rs
  s   &    rm   test_brunnermunzel_default,TestBrunnerMunzel.test_brunnermunzel_default!  s    $$TVVTVV4$$TVVTVV4B0@0@AB 2(,(8(8	:B 3(,(8(8	:B 5(,(8(8	:rp   c           	         R pRpRp\        VR9  4       \        \        \        P                  V P
                  V P                  VVV4       R# )r  r  r  N)r  r  r  r   r   r   r[   r)  rZ   rh
  rc   r  distributionr   s   &   rm   $test_brunnermunzel_alternative_error6TestBrunnerMunzel.test_brunnermunzel_alternative_error"  sI     
#CCDj))ffff!" 	"rp   c                   \         P                  ! V P                  V P                  R R7      w  r\         P                  ! V P                  V P                  R R7      w  r4\	        W$V P
                  R7       \	        VRV P
                  R7       \	        VRV P
                  R7       \	        VRV P
                  R7       R# )r  r7  r  r'  g "H[?Nr(  r.  rs
  s   &    rm   $test_brunnermunzel_distribution_norm6TestBrunnerMunzel.test_brunnermunzel_distribution_norm"  s    $$TVVTVV(K$$TVVTVV(KB0@0@AB 2(,(8(8	:B 3(,(8(8	:B 5(,(8(8	:rp   c           	         R pRpRp\        VR9  4       \        \        \        P                  V P
                  V P                  VVV4       R# )r  r  r  N)r  r  r5  r6  s   &   rm   %test_brunnermunzel_distribution_error7TestBrunnerMunzel.test_brunnermunzel_distribution_error"  sH    ! 
?23j))ffff!" 	"rp   kwarg_updaterg   rf   c                |   R V P                   RV P                  /pVP                  V4       \        P                  ! \
        \        R7      ;_uu_ 4        \        P                  ! R/ VB w  r4RRR4       \        X\        P                  4       \        X\        P                  4       R#   + '       g   i     LF; i)rf   rg   r   Nr   )rZ   rh
  r  r   rb  r   r   r[   r)  r   r   rb   )rc   rA  r@  r>  r=  s   &&   rm   test_brunnermunzel_empty_imput0TestBrunnerMunzel.test_brunnermunzel_empty_imput+"  s{     tvvsDFF+l#\\,4IJJ % 3 3 =f =I KY'VRVV$ KJs   B++B;	c                   ^^^^^^^^^^^^^^\         P                  .p. ROp\        P                  ! WRR7      w  r4\        P                  ! W!RR7      w  rV\	        V\         P                  4       \	        V\         P                  4       \	        V\         P                  4       \	        V\         P                  4       R# )rW   r  r   Nr   r   r   r   rW   rE   r   rW   rW   rw   r   )r   rb   r[   r)  r   rc   rZ   rh
  rj
  r  rk
  r	  s   &      rm   &test_brunnermunzel_nan_input_propagate8TestBrunnerMunzel.test_brunnermunzel_nan_input_propagate5"  s    1aAq!Q1aArvv>-$$QkB$$QkBR R R R rp   c                    ^^^^^^^^^^^^^^\         P                  .p. ROpRpRpRp\        \        \        P
                  VVVVV4       \        \        \        P
                  VVVVV4       R# )rW   r  r  r   NrF  )r   rb   r   r   r[   r)  )rc   rZ   rh
  r  r7  r   s   &     rm   "test_brunnermunzel_nan_input_raise4TestBrunnerMunzel.test_brunnermunzel_nan_input_raise@"  s    1aAq!Q1aArvv>-!
j))!" 	" 	j))!" 	"rp   c                r   ^^^^^^^^^^^^^^\         P                  .p. ROp\        P                  ! WRR7      w  r4\        P                  ! W!RR7      w  rV\	        WFV P
                  R7       \	        VRV P
                  R7       \	        VRV P
                  R7       \	        VRV P
                  R7       R# )	rW   r   r   r  r'  r-  NrF  r(  )r   rb   r[   r)  r	   r  rG  s   &      rm   !test_brunnermunzel_nan_input_omit3TestBrunnerMunzel.test_brunnermunzel_nan_input_omitV"  s    1aAq!Q1aArvv>-$$Qf=$$Qf=B0@0@AB 2(,(8(8	:B 3(,(8(8	:B 5(,(8(8	:rp   c                    . ROp. ROpRp\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! WRR7       RRR4       R#   + '       g   i     R# ; i)zktests that a warning is emitted when p is nan
p-value with t-distributions can be nan (0/0) (see gh-15843)
zDp-value cannot be estimated|divide by zero|invalid value encounteredr   r  r;  Nr  r  )r   rb  r   r[   r)  r  s   &   rm   test_brunnermunzel_return_nan/TestBrunnerMunzel.test_brunnermunzel_return_nand"  sC     T\\.4437 5444s   AA#	c                    . ROp. ROp\         P                  ! \        RR7      ;_uu_ 4        \        P                  ! WRR7      w  r4RRR4       \        X^ 4       R#   + '       g   i     L; i)z^tests that a p is 0 for datasets that cause p->nan
when t-distribution is used (see gh-15843)
zdivide by zeror   r  r;  Nr  r  )r   rb  r   r[   r)  r   )rc   rf   rg   r  re  s   &    rm   test_brunnermunzel_normal_dist0TestBrunnerMunzel.test_brunnermunzel_normal_disto"  sN     \\.0@AA&&q(CDA BQ BAs   AA.	r   N)rW   rE   rW   rW   rW   rW   rW   rW   rW   rW   rE   r   rW   rW   rF  )r   r   r   r   rZ   rh
  r  r*  r/  r2  r8  r<  r?  r   r   r  rC  rH  rK  rN  rQ  rT  r   r   r   s   @rm   r%  r%  !  s     2A)AK:.::"	:" [[^sBi#r/2BR.@.B C%C%	!",:	8	 	rp   r%  c                     a  ] tR tRt o RtR t]P                  P                  R. RO. RORR]	P                  ) RR	.R
RR]	P                  R..4      R 4       t]P                  P                  R. RO. RO.4      R 4       t]P                  P                  RRR.4      ]P                  P                  RR	R.4      ]P                  P                  RRR.4      R 4       4       4       tR tRtV tR# )TestQuantileTesti{"  zYTest the non-parametric quantile test,
including the computation of confidence intervals
c                   . ROpRp\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! V.4       RRR4       Rp\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! V^^.R7       RRR4       Rp\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! VRR.R	7       RRR4       \         P                  ! \        VR7      ;_uu_ 4        \        P                  ! V^R	7       RRR4       \         P                  ! \        VR7      ;_uu_ 4        \        P                  ! VRR	7       RRR4       R
p\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! VRR7       RRR4       Rp\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! V4      P                  ^4       RRR4       R#   + '       g   i     EL; i  + '       g   i     EL; i  + '       g   i     EL`; i  + '       g   i     EL/; i  + '       g   i     L; i  + '       g   i     L; i  + '       g   i     R# ; i)rW   z/`x` must be a one-dimensional array of numbers.r   Nz`q` must be a scalar.)r@  z-`p` must be a float strictly between 0 and 1.r1   r  )re  z`alternative` must be one of...z	one-sidedr  r.  r  ro  )r   r   r   r[   quantile_testr  )rc   rf   r  s   &  rm   test_quantile_test_iv&TestQuantileTest.test_quantile_test_iv"  s   C]]:W55$ 6 *]]:W55aV, 6 B]]:W55c4[1 6]]:W55Q' 6]]:W55T* 6 4]]:W55{; 6 I]]:W55"66q9 65) 655 655 65555555 65 655sS   H1H:H,I II'&I:H	H)	,H=	 I	I$	'I7	:J	zp, alpha, lb, ub, alternativern  rF  r  g{gA?r  r@  gg @r  c                    \         P                  ! \         P                  ! ^ RR4      4      p\        P                  ! WaVR7      p\        VP                  V4      W4.RR7       R# )ry   r  r  )re  r  rD  r  N)r   r  r   r[   rY  r
   r  )rc   re  r1  lbubr  rf   r   s   &&&&&&  rm   test_R_ci_quantile#TestQuantileTest.test_R_ci_quantile"  sJ      FF299Qd+,!!!kB//6uMrp   zq, p, alternative, refc                    \         P                  ! \         P                  ! ^ RR4      4      p\        P                  ! WQW#R7      p\        VP                  VRR7       R# )ry   r  r  r@  re  r  r  r  N)r   r  r   r[   rY  r
   r=  )rc   r@  re  r  r  rf   r   s   &&&&&  rm   test_R_pvalueTestQuantileTest.test_R_pvalue"  sA     FF299Qd+,!!!AG

Ce4rp   r  
continuousdiscreter  r1  c                   \        ^\        V4      ,          \        V4      ,           V,          4      p\        P                  P	                  V4      pVR8X  d(   VP                  ^R7      w  rgVP                  ^dR7      pM6VP                  ^^^dR7      pVP                  4       pVP                  ^^4      p\        P                  ! WWbR7      p	V	P                  VR7      p
VR8X  d   WP                  8*  pMWP                  8  pW,           F5  p\        P                  ! WWbR7      p	V	P                  ^V,
          8  d   K5  Q h	  W( ,           F5  p\        P                  ! WWbR7      p	V	P                  ^V,
          8  d   K5  Q h	  R# )rJ   re  r  rb  r(  r  N)r!  r   r   r  r  rX	  r[   rY  r  r  r  r=  )rc   r  r  r1  r  r  re  r@  r  r   r  i_insiderf   s   &&&&         rm   test_pval_ci_match#TestQuantileTest.test_pval_ci_match"  sG    As4yL3{#33U:;ii##D)<::1:%DA**#*&C,,q"3,/C

AQ#A!!#aI$$e$< & gg~Hff}HA%%c!MC::E	)))  YA%%c!MC::E	)))  rp   c                \   . ROpRp\         P                  ! V^RRR7      p\        VP                  VRR7       ^;.^,          ^=.^h,          ,           p\         P                  ! R^pR7      P                  ^R	7      p\         P                  ! V^<RR
R7      p\        VP                  VRR7       R# )   geX?r  r  rb  r
  r  r1   )re  r  r  r  r  rE  N)rl                                   r@        )r[   rY  r
   r=  r   r_  )rc   rf   pvalue_expectedr   s   &   rm   test_match_conover_examples,TestQuantileTest.test_match_conover_examples"  s     !!!sdL

O$? DFbT5\!++s377!7<!!!rSiH

O%@rp   r   N)rG  rn  gX݊?g蜶?r  )r1   rF  g-tA?gP"?r  )rt  rG  r  gͯI	?)r  r1   r  gɍQ%e?)r   r   r   r   r5  rZ  r   r   r  r   r!  r_  rc  ri  r{  r   r   r   s   @rm   rW  rW  {"  s    :6 [['	G	F
rvvg/	8
s%rvvy	9	;NN [[ 	2	1	3
5
5 [[VlJ%?@[[]VY,?@[[WsDk2$* 3 A A$*LA Arp   rW  c                      a  ] tR tRt o ]P
                  P                  ^ 4       ]P
                  P                  ^^4      t]P
                  P                  ^
^4      t	RRRR]3RRRR]	3RR	RR. R&O. R'O. R(O.3R
RRR. R)O. R*O. R+O.3RRRR. R,O. R,O. R,O. R,O. R,O. R,O. R,O. R,O. R-O. R.O. R.O. R.O. R.O. R.O.3^RRR. R/O. R/O. R/O. R/O. R/O. R/O. R/O. R/O. R/O. R/O. R/O. R/O. R/O. R0O. R1O. R1O. R1O. R1O. R1O. R1O. R1O.3^RRR. R2O. R2O. R3O.3RRRR. R4O. R4O. R4O. R4O. R4O. R4O. R5O. R6O. R6O. R6O.
3^RRR. R/O. R/O. R/O. R/O. R/O. R/O. R/O. R/O. R/O. R/O. R/O. R/O. R0O. R1O. R1O. R1O. R1O. R1O. R1O.3RRRR. R7O. R7O. R8O. R9O.3^uRRR. R/O. R/O. R/O. R/O. R/O. R/O. R/O. R/O. R/O. R0O. R1O.3.t
]P                  P                  R]
4      R 4       tRRRR. R:O. R;O.3RRRR. R:O. R:O. R:O. R<O. R=O.3RRRR. R>O. R>O. R>O. R>O. R>O. R>O. R>O. R>O. R>O. R?O. R@O. R@O. R@O. R@O. R@O.3.t]P                  P                  R]
4      ]P                  P!                  4       R  4       4       tR! tR" tR# tR$tV tR%# )ATestPageTrendTesti#  i2  g:hў?Fr  i  gsH?i,0  gY@?i
  gXY?r  iL  gs˜?TgĞ?g>K=?i  gqူ?ga?i  g;?g[^6?zL, p, ranked, method, datac                    \         P                  P                  ^*4       \        P                  ! WSVR7      p\        WP                  4       \        W&P                  4       \        WFP                  4       R# r  )rankedr  N
r   r  r  r[   page_trend_testr   r>  r
   r=  r  rc   Lre  r  r  r  r   s   &&&&&& rm   test_accuracyTestPageTrendTest.test_accuracyE#  sH    
		r##DGQ&::&VZZ(rp   i  g-lpW?i*  gh[?i  g&]2?c                    \         P                  P                  ^*4       \        P                  ! WSVR7      p\        WP                  4       \        W&P                  4       \        WFP                  4       R# r  r  r  s   &&&&&& rm   test_accuracy2 TestPageTrendTest.test_accuracy2b#  sJ     			r##DGQ&::&VZZ(rp   c                b   \         P                  P                  ^*4       ^
^r!\         P                  ! ^V^,           4      p\         P                  P	                  \         P                  ! V4      4      p\         P                  P                  W4      p\        P                  ! V^R7      p\        P                  ! V4      p\        P                  ! VRR7      p\        P                  ! VRR7      p	\        P                  ! WcR7      p
\        P                  ! VRV3,          W4,          R7      p\        VP                  VP                  4       \        VP                  V	P                  4       \        VP                  V
P                  4       \        VP                  VP                  4       R# )r  r>   Tr  F)predicted_ranksr   N)r   r  r  r   r  r  r[   rankdatar  r   r>  )rc   r  r  r  permr  ranksr  r  r  res4res5s   &           rm   test_optionsTestPageTrendTest.test_optionsk#  s   
		r21))Aqs+yy$$RYYq\2yy~~a#t!,$$U+$$U48$$T%8$$UL$$U1d7^5D5JLT^^T^^4T^^T^^4T^^T^^4T^^T^^4rp   c                   \         P                  P                  ^*4       . R
O. RO. RO. RO. RO. RO.p\         P                  ! V4      P                  p\         P
                  ! ^^4      p\        P                  ! VRVRR7      p\        VP                  R4       \        VP                  R^R7       \        P                  ! VRVRR7      p\        VP                  R4       \        VP                  R^R7       R	# )r  Fr  )r  r  r  i  gy&1l?rW  r  gHPsb?N)rC  u   o   )rL  r!  k   )g      y   )rD        )         )   r
  t   )r   r  r  r   r   r   r[   r  r   r>  r   r=  )rc   r  r  r   s   &   rm   test_Ames_assay!TestPageTrendTest.test_Ames_assay}#  s    
		r/Cxx~))Aq/##D4C+79 	S]]C(CJJ:##D4C+24 	S]]C(CJJ:rp   c                *
   \        \        R R7      ;_uu_ 4        \        P                  ! R4       RRR4       \        \        R R7      ;_uu_ 4        \        P                  ! . 4       RRR4       \        \        R R7      ;_uu_ 4        \        P                  ! ^^.4       RRR4       \        \        R R7      ;_uu_ 4        \        P                  ! ^...4       RRR4       \        \        RR7      ;_uu_ 4        \        P                  ! \        P
                  P                  ^^4      4       RRR4       \        \        RR7      ;_uu_ 4        \        P                  ! \        P
                  P                  ^^4      4       RRR4       Rp\        \        VR7      ;_uu_ 4        \        P                  ! . RO. RO.. ROR7       RRR4       \        \        VR7      ;_uu_ 4        \        P                  ! . RO. RO.. ROR7       RRR4       \        \        VR7      ;_uu_ 4        \        P                  ! . RO. RO.. ROR7       RRR4       \        \        VR7      ;_uu_ 4        \        P                  ! . RO. RO.RR7       RRR4       \        \        RR7      ;_uu_ 4        \        P                  ! . RO. RO.R4       RRR4       \        \        RR7      ;_uu_ 4        \        P                  ! . RO. RO.R4       RRR4       \        \        R	R7      ;_uu_ 4        \        P                  ! . RO^^\        P                  ..R
R7       RRR4       \        \        RR7      ;_uu_ 4        \        P                  ! . RO. RO.RR7       RRR4       \        \        RR7      ;_uu_ 4        \        P                  ! . RO. RO.RR7       RRR4       R#   + '       g   i     EL; i  + '       g   i     EL; i  + '       g   i     ELw; i  + '       g   i     ELP; i  + '       g   i     EL; i  + '       g   i     EL; i  + '       g   i     EL; i  + '       g   i     ELn; i  + '       g   i     EL@; i  + '       g   i     EL; i  + '       g   i     EL; i  + '       g   i     EL; i  + '       g   i     EL; i  + '       g   i     ELW; i  + '       g   i     R# ; i)z`data` must be a 2d array.r   NzPage's L is only appropriatez+`predicted_ranks` must include each integer)r  r  r  z`data` is not properly rankedTz`data` contains NaNsFr  z`method` must be inekki)r  r  z`ranked` must be boolean.)r  r  r  r  )r  rE   r   )rW   rE   r   r   )ry   rE   r   r  )	r   r   r[   r  r   r  r  rb   r&  r;  s   & rm   r  'TestPageTrendTest.test_input_validation#  sK   :-IJJ!!$' K:-IJJ!!"% K:-IJJ!!1a&) K:-IJJ!!QC5'* K :-KLL!!"))..A"67 M:-KLL!!"))..A"67 M @:W55!!	9'=2;= 6 :W55!!	9'=2=? 6 :W55!!	9'=2>@ 6 :W55!!	9'=2;= 6
 :-LMM!!9i"8$? N:-LMM!!9i"8$? N :-CDD!!9q!RVVn"=).0 E :-BCC!!	9'=)/1 D 9,GHH!!	9'=)/1 IHW KJJJJJJJJJJJ MLLLLL
 655 655 655 655
 NMMMMM EDD DCC IHHs   O)O=
PP%?5P95Q-!Q!/!Q51!R	3R3R12S1.S S- T)O:	=P	P"	%P6	9Q
	Q	!Q2	5R		R	R.	1S	S	S*	-S>	T	r   N)rO  rM  I   ru  rM  `   r  ;   r,
  $   rK  1   rJ  +   rY  rM     r  rP  r  rK   r  rH     r  )D   4   rD  "   rf	  r  A   X   rL   rJ  rQ     r  C   E   ^   r  r  r  W   rY  r  r  r  r  )rJ  rR   U   ru  O   rQ   \   V   rL   @   r-
  r  r  rg	  r-
  Y   r7  r  r  r  6   rR   B   3   r  )r2   r   g @rw   r  rP   )rw   r   r  rO   r  rL   )r  r
  rO   rQ   rM   r  )r   r   rE   rW   )r   r   rW   rE   r  )r   rE   rW   rx  r  )rz   rw   r   r   rE   rW   )rW   r   r   rw   rE   rz   )rw   r   r   rE   rW   )r   rW   r   rE   rw   r  )rJ   rz   rw   r   r   rE   rW   )rz   rw   rJ   r   r   rE   rW   r  )
rO   rI   rF   rJ   rz   rw   r   r   rE   rW   )
rW   rF   r   rJ   rz   rw   rI   r   rE   rO   )
rI   rE   rF   rJ   rz   rw   r   r   rO   rW   rH  )rF   rJ   rz   rw   r   r   rE   rW   )rW   r   rw   rz   r   rJ   rE   rF   r  )r   r   r   r   r   r  r  r  	data_3_25
data_10_26tsr   r   r  r  ts2r  r  r  r  r  r   r   r   s   @rm   r~  r~  #  s      IINN1		q"%IB'J $e\9
E%ulJ
G$e\===	>? %ug%#&() "D',l,l,l,()
 "D'y)Y	9y)Y	9y)Y	9y)-.
 "D' 24FGI"D'_o_o_o
 "D'y)Y	9y)Y	9y)Y	9
 !4!#8!#8:; "D'y)Y	9y)Y	CDO*
BX [[92>) ?) #T7,,./ $dG,.M,.M,./ $dG%'?%'?%'?%'?%'?%'?%'?%'(C* [[92>[[)  ?)5$;*/1 /1rp   r~  iv5z	fun, argsc           	         V ! VR R/ pV ! VRR/ p\        W#4       V P                   R2p\        P                  ! \        \
        P                  ! V4      R7      ;_uu_ 4        V ! VR RRR/  RRR4       R#   + '       g   i     R# ; i)r  r  r  z#() got multiple values for argumentr   N)r   r   r   r   r&  reescape)r;  r?  r   r  errs   &&   rm   test_rename_mode_methodr  #  su     t
$G
$C#7#Dll^>
?C	y		#	7	7T0'00 
8	7	7	7s   #A88B		c                   
  a  ] tR tRt o R tR tR tR t]P                  P                  R. RO4      ]P                  P                  R^R.4      R	 4       4       t]P                  P                  R^R.4      R
 4       tRtV tR# )TestExpectilei#  c                    \         P                  P                  ^*4      pVP                  ^R7      p\        \        P
                  ! VRR7      \         P                  ! V4      4       R# )r  r  r1   r1  N)r   r  r  r
   r[   	expectiler^   rc   r  rf   s   &  rm   test_same_as_meanTestExpectile.test_same_as_mean#  sC    ii##B'JJBJ5rwwqzBrp   c                    \         P                  P                  ^*4      pVP                  ^R7      p\        \        P
                  ! V^ R7      \         P                  ! V4      4       R# r  r  r  N)r   r  r  r
   r[   r  aminr  s   &  rm   test_minimumTestExpectile.test_minimum#  C    ii##B'JJBJ3RWWQZ@rp   c                    \         P                  P                  ^*4      pVP                  ^R7      p\        \        P
                  ! V^R7      \         P                  ! V4      4       R# r  )r   r  r  r
   r[   r  amaxr  s   &  rm   test_maximumTestExpectile.test_maximum#  r  rp   c                  a	 \         P                  P                  R 4      pR o	V	3R lp^
pVP                  V4      pVP                  4       pVP                  V4      p\        P                  ! WEVR7      pV! WEV4      p\        Wx4       R# )l   b@lN c                     \         P                  ! WR 7      p^V,
          WAV 8*  &   \         P                  ! WC,          W,
          ^,          ,          4      # )r  )r   r  r^  )r  rK  r1  r
  r  s   &&&& rm   r;  'TestExpectile.test_weights.<locals>.fun#  s;    Q1AE	A1fI66!+
233rp   c                    < \         P                  ! V 4      \         P                  ! V 4      3p\        P                  ! SVWV3R 7      P
                  # ))bracketr?  )r   r  r  r   minimize_scalarrf   )rK  r1  r
  r  r;  s   &&& rm   
expectile2.TestExpectile.test_weights.<locals>.expectile2#  sC    ffQi*G++C23G1DFFGaHrp   r
  N)r   r  r  r[   r  r
   )
rc   r  r  r  rK  r1  r
  r   r  r;  s
   &        @rm   test_weightsTestExpectile.test_weights#  su    
 ii##$78	4
	H
 JJqM

**Q-ooa87+!rp   r1  r  r9  c                   \         P                  P                  ^*4      pVP                  VR7      pR
 F:  p\	        \
        P                  ! \         P                  ! W%R7      VR7      V4       K<  	  VP                  4       p\	        \
        P                  ! WE,           VR7      \
        P                  ! WAR7      V,           4       \	        \
        P                  ! WE,
          VR7      \
        P                  ! WAR7      V,
          4       \	        \
        P                  ! WT,          VR7      V\
        P                  ! WAR7      ,          4       VP                  V^
R7      pVR8X  d   R pMVR8  d   R pMR pV! \
        P                  ! \         P                  WF,           ,          VR7      \
        P                  ! WAR7      \
        P                  ! WaR7      ,           4       VP                  V^R7      p\
        P                  ! WAR7      \
        P                  ! WaR7      8:  g   Q hVP                  V^
R7      pR F  pV! \
        P                  ! ^V,
          V,          WV,          ,           VR7      ^V,
          \
        P                  ! WAR7      ,          V\
        P                  ! WaR7      ,          ,           4       K  	  \	        \
        P                  ! V) VR7      \
        P                  ! V^V,
          R7      ) 4       R	# )ub  
See Section 6 of
I. Steinwart, C. Pasin, R.C. Williamson & S. Zhang (2014).
"Elicitation and Identification of Properties". COLT.
http://proceedings.mlr.press/v35/steinwart14.html

and

Propositions 5, 6, 7 of
F. Bellini, B. Klar, and A. Müller and E. Rosazza Gianin (2013).
"Generalized Quantiles as Risk Measures"
http://doi.org/10.2139/ssrn.2225751
r  r1   )r  r  r  rx  c                     \        W4       R # r  )r
   rK  rW  s   &&rm   	assert_op:TestExpectile.test_expectile_properties.<locals>.assert_op=$  s
    %rp   c                     W8  g   Q hR # r  r   r  s   &&rm   r  r  A$      uurp   c                     W8  g   Q hR # r  r   r  s   &&rm   r  r  E$  r  rp   N)r  ry   r1   )rD  r1   r@  )r   r  r  r  r
   r[   r  r~   exponentiallogisticr_)rc   r1  r  r  rf   rj  rg   r  s   &&&     rm   test_expectile_properties'TestExpectile.test_expectile_properties$  s'   $ ii##B'JJAJ
 Aa >eL  OOOOAE/OOA+a/	
 	OOAE/OOA+a/	
 	OOAE///	
 LLaRL(C<& S[ 	OOBEE!%L6OOA+ooa-.	
 JJA1J%OOA+uq/NN	
N LLaRL( A1a!#U;177EOOA334 ! 	OOQBe,__Qag..	
rp   c                   \         P                  P                  ^*4      pVP                  ^VR7      p. p\         P                  ! R\         P
                  ! R4      ^d4      p\         P                  ^ V^VRRR1,          ,
          ^3,           F)  pVP                  \        P                  ! W6R7      4       K+  	  \         P                  ! \         P                  ! V4      ^ 8  4      '       g   Q hR# )r  )rK  r  r1   Nr  r  rU   )r   r  r  paretologspacelog10r  rI  r[   r  r  diff)rc   r  r  rf   e_list	alpha_seqr1  s   &&     rm   test_monotonicity_in_alpha(TestExpectile.test_monotonicity_in_alphai$  s    ii##B'JJJ#KKRXXc]C8	UU1iYv2v->)>ABBEMM%//!9: Cvvbggfo)****rp   r   N)r4  g?r1   g/#    ?r@  )r   r   r   r   r  r  r  r  r   r   r  r  r  r   r   r   s   @rm   r  r  #  s     C
A
A
"4 [[: [[S2t*-_
 ._
B [[S2t*-+ .+rp   r  c            	       \  a  ] tR tRt o . RNRNRNRNRNRNRNRNRNR	NR
NRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNR NR!NR"NR#NR$NR%NR&NR'NR(NRNR)NRNR*NR+NR,NR-NR.NR/NR0NR1NR'NR2NR3NR(NR4NR-NR5NR6NR7NR8NR9NR:NR;NR<NR=NR>NRNR4NR?NRNR@NRANR;NRNRBNRCNR3NRDNRENR	NRNRFNRGNRHNRINRNRNRJNRKNRENRLNRMNR%NRDNRNRNNRONRPNRKNR6NRQNRNRRNRSNRTNRUNRNRVNRNRWNRXNRNR)NR#NRYNRZNRNR[NtR. RmO]P                  ]P                  R\.tR] t	]
R^ 4       t]P                  P                  R_]^ Rn. . RoO..,           4      R` 4       t]P                  P                  Ra]4      Rb 4       t]P                  P                  Rc]4      Rd 4       t]P                  P                  Re]4      Rf 4       t]P                  P                  R_^^. RpO.4      ]P                  P                  ReRgRh.4      ]P                  P                  RcRgRh.4      Ri 4       4       4       tRj tRktV tRl# )qTestLMomentiu$  gףp=
?gp=
ף?r2   r
  r  r1   r   rr  r
  g{Gz?g@g(\?gףp=
?g
ףp=
?g)\(?gRQ @rt  g{Gz?gffffff @r  g{Gz@gRQ?gGz@gQ?g(\?gzG?g
ףp=
?gQ?gffffff?gGz
@g(\?g(\?gQ?gq=
ףp?g(\@gQ?gGz	@r%  gQ?gp=
ף @gp=
ף@gq=
ףp@gRQ?gGz?g
ףp=
?rE  gHzG?g      @gQ?r  gRQ?gQ?gp=
ף?gQ@gGz?gQ?gp=
ף?gq=
ףp?r
  gp=
ף?gQ?g@g)\( @gzG@gGz?g(\?g333333?g)\(?gGz@r@  g(\?g=
ףp=?gHzG?g{Gz?g
ףp=
?gףp=
?gQ?r	  g?g(\?gQ?gffffff@gQ?g?gGz?g{Gz?gHzG@g\(\?g(\?g(\?za duckc           	        R p\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! \
        P                  ! V P                  \
        P                  R7      4       RRR4       R#   + '       g   i     R# ; iz*`sample` must be an array of real numbers.r   r6   N)	r   r   r   r[   lmomentr   r   r  r  r;  s   & rm   test_dtype_ivTestLMoment.test_dtype_iv$  sF    >]]:W55MM"((499BMMBC 6555s   AA66B	c           	         R p\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! \
        P                  ! V P                  \        R7      4       RRR4       R#   + '       g   i     R# ; ir  )	r   r   r   r[   r  r   r   r  r;  r;  s   & rm   test_dtype_iv_non_numeric%TestLMoment.test_dtype_iv_non_numeric$  sB    >]]:W55MM"((499F;< 6555s   ;A,,A=	rw  c                    R p\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! V P
                  VR7       RRR4       R#   + '       g   i     R# ; i)z*`order` must be a scalar or a non-empty...r   r  Nr   r   r   r[   r  r  )rc   rw  r  s   && rm   test_order_ivTestLMoment.test_order_iv$  s9    >]]:W55MM$))51 6555   #AA%	r?   c                    R p\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! V P
                  VR7       RRR4       R#   + '       g   i     R# ; i)z"`axis` must be an integer, a tupler   r>   Nr	  )rc   r?   r  s   && rm   test_axis_ivTestLMoment.test_axis_iv$  s9    6]]:W55MM$))$/ 6555r  sortedc                    R p\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! V P
                  VR7       RRR4       R#   + '       g   i     R# ; i)z`sorted` must be True or False.r   )r  Nr	  )rc   r  r  s   && rm   test_sorted_ivTestLMoment.test_sorted_iv$  s9    3]]:W55MM$))F3 6555r  standardizec                    R p\         P                  ! \        VR7      ;_uu_ 4        \        P                  ! V P
                  VR7       RRR4       R#   + '       g   i     R# ; i)z$`standardize` must be True or False.r   )r  Nr	  )rc   r  r  s   && rm   test_standardize_ivTestLMoment.test_standardize_iv$  s9    8]]:W55MM$))= 6555r  FTc                p   \         P                  ! . RO4      pV'       g   VR;;,          V^,          ,          uu&   V'       d!   \         P                  ! V P                  4      MV P                  p\        P
                  ! WQW#R7      p\        Wd\         P                  ! V4      ^,
          ,          4       R# )0ʻEH?r  )r  r  N)r  gk?gz[?g+3 ?)r   rY   r  r  r[   r  r
   )rc   rw  r  r  r  r  r   s   &&&&   rm   test_lmomentTestLMoment.test_lmoment$  su     jj B C Gs1vG%+rwwtyy!mmD[PE!21!456rp   c                   \         P                  p\         P                  ! V P                  4      p\        P
                  ! VP                  V4      4      p\        P
                  ! V4      pVP                  P                  V8X  g   Q h\        W4R R7       \         P                  p\         P                  ! . RO4      p\        P
                  ! VP                  V4      4      p\        P
                  ! VP                  \         P                  4      4      pVP                  P                  \         P                  8X  g   Q h\        W4RR7       R# )r  r  rD  Nr  )r   r   rY   r  r[   r  r  r7   r  r
   int64r   )rc   r7   sampler   r  s   &    rm   
test_dtypeTestLMoment.test_dtype$  s    

DII&mmFMM%01mmF#yy~~&&&t,O,mmFMM%01mmFMM"**56yy~~+++u-rp   r   N)rW   rE   r  rU   r  r  )r   r   r   r   r  r   rb   r!  not_integersr  r%   r  r   r   r  r
  r  r  r  r  r  r   r   r   s   @rm   r  r  u$  sd    
ND 
N$ 
N 
Nc 
N3 
N 
Nc 
N3 
N 
ND 
N# 
N
N
N
N"
N$(
N*.
N04
N69
N;?
NAE
NGK
N
N
N
N"
N$(
N*.
N04
N6:
N<@
NBF
NHL
N 
N 
N 
N #
N %)
N +/
N 15
N 7;
N =A
N CG
N IM
N 	
N 	
N 	
N #	
N %)	
N +/	
N 14	
N 6:	
N <@	
N BF	
N HL	
N
 
N
 
N
 
N
 #
N
 %)
N
 +/
N
 15
N
 7;
N
 =A
N
 CG
N
 IM
N 
N 
N 
N "
N $(
N *.
N 04
N 6:
N <@
N BF
N HL
N 
N 
N 
N #
N %)
N +/
N 15
N 7;
N =@
N BF
N HL
N 
N 
N 
N #
N %)
N +/
N 15
N 7;
N =A
N CG
N IM
N 
N 
N 
N "
N $(
N *.
N 04
N 6:
N <@
N BF
N HL
N 
N 
N 
N #
N %)
N +/
N 15
N 7;
N =A
N CG
N IM
ND bffbffh?LD
 = =
 [[WlaR)5M&MN2 O2
 [[V\20 30
 [[X|44 54
 [[]L9> :>
 [[Wq!\&:;[[]UDM:[[Xt}57 6 ; <7". .rp   r  c                   $  a  ] tR tRt o ]P
                  P                  R. RO4      ]P
                  P                  RRR.4      ]P
                  P                  RRR.4      R 4       4       4       tR	 t]P
                  P                  R
4      ]P
                  P                  R4      R 4       4       t
]P
                  P                  R4      R 4       t]! RR7      R 4       tR t]P
                  P                  R4      R 4       tR tR tRtV tR# )TestXP_Meani$  r?   Nr
  Tr  Fc                   \         P                  P                  R 4      pVP                  R4      pVP                  V4      pR;rV'       d;   VP                  R4      pVP                  V4      p	\         P                  ! Wh4      w  rh\        WyW$R7      p
\         P                  ! WhW$R7      p\        WP                  V4      4       R# )   -fH N)r
  r?   r  r  rv   )r   r  r  rY   r  r!   r7  r/   )rc   rd   r?   r
  r  r  rf   x_xpr  w_xpr   r  s   &&&&&       rm   test_xp_mean_basicTestXP_Mean.test_xp_mean_basic$  s     ii##N3JJy!zz!}

6"A::a=D&&q,DAtHjjDDZZ_-rp   c                    VP                  R 4      VP                  ^4      r2Rp\        P                  ! \        VR7      ;_uu_ 4        \        W#R7       RRR4       R#   + '       g   i     R# ; i)r   z/Array shapes are incompatible for broadcasting.r   r
  N)r   rY  r   r   r   r!   )rc   rd   rf   r  r  s   &&   rm   test_non_broadcastable"TestXP_Mean.test_non_broadcastable$  sF    yy~rxx{1C]]:W55Q" 6555s   AA0	r  r  c                   VP                  . RO4      p\        VP                  . RO4      VR7      p\        W1P                  VP                  4      4       \        VP                  . RO4      VR7      p\        W1P                  \        P
                  ) 4      4       \        VP                  . RO4      VR7      p\        W1P                  \        P
                  4      4       R# )r   r
  Nr8  r  )r   r   r   )r   r   r   )rY   r!   r/   rb   r   r!  )rc   rd   r
  r   s   &&  rm   test_special_casesTestXP_Mean.test_special_cases$  s     **]+rzz,/AZZ/0rzz,/AZZ01rzz,/AZZ/0rp   r	  c                   VP                  R 4      pV^8H  pVP                  W1P                  V4      p\        V4      '       d<   \        P
                  ! \        RR7      ;_uu_ 4        \        VRR7       RRR4       M:\        P
                  ! \        RR7      ;_uu_ 4        \        VRR7       RRR4       \        V4      p\        VRR7      pVP                  VP                  4      p\        WF4       \        WV4       \        VRR7      pVP                  W#( ,          4      p\        Wv4       VP                  ^
4      pVP                  W1P                  V4      p\        VP                  R 4      VRR	7      pVP                  W#( ,          4      p\        Wv4       R#   + '       g   i     L; i  + '       g   i     EL; i)
r   r	  r   r   r   Nr   r  r   )r
  r   )r   rP  rb   r(   r   r   r&  r!   r   rY   r0   r^   r/   r  )	rc   rd   rf   r  r  r  r  r   r
  s	   &&       rm   r  TestXP_Mean.test_nan_policy$  sO    IIcNQHHT661% y0OPPw/ QP z1PQQw/ R {k2jj "" qV,ggah! ''"+((41ryy~w6Jggah!/ QP RQQs   (F!#F4!F1	4G	r  c                ~   VP                  R 4      pVP                  V^8H  VP                  V4      pRp\        P                  ! \
        VR7      ;_uu_ 4        \        V\        P                  ,          RR7      pVP                  VP                  4      p\        WE4       RRR4       R#   + '       g   i     R# ; ir   zAfter omitting NaNs...r   r   r   N)
r   rP  rb   r   rb  r   r!   r   rY   r0   rc   rd   rf   r  r   r  s   &&    rm   test_nan_policy_warns!TestXP_Mean.test_nan_policy_warns%  s~    IIcNHHQ!VRVVQ' +\\.881rvv:&9C**RVV$CC% 9888   A	B++B<	c                   R p\         P                  ! \        VR7      ;_uu_ 4        \        VP	                  . 4      4      pVP	                  VP
                  4      p\        W44       RRR4       Rp\         P                  ! \        VR7      ;_uu_ 4        \        VP	                  . .4      ^R7      pVP	                  VP
                  .4      p\        W44       RRR4       \        VP	                  . .4      ^ R7      pVP	                  . 4      p\        W44       R#   + '       g   i     L; i  + '       g   i     L^; iz,One or more sample arguments is too small...r   Nz2All axis-slices of one or more sample arguments...r>   )r   rb  r   r!   rY   rb   r0   rc   rd   r  r   r  s   &&   rm   r  TestXP_Mean.test_empty%%  s    @\\,G<<2::b>*C**RVV$CC% =
 G\\,G<<2::rd+!4C**bffX&CC% =
 rzz2$'a0jjn! =< =<   ADAD1D.	1E	4ignore:overflow encountered in reduce:RuntimeWarningc           	        VP                  VP                  4      P                  p\        P                  ! W".\        P                  R 7      pVP	                  V4      p\        P
                  ! RR7      ;_uu_ 4        \        V4      p\        P                  ! V4      p\        P                  P                  V\        P                  4       \        WQP	                  V4      4       RRR4       \        WAP                  R 7      pVP	                  \        P                  ! \        P                  ! V\        P                  R 7      4      4      p\        WV4       R#   + '       g   i     L|; i)r6   r}  )overN)r   r   r  r   rY   r  r!   r^   r"  r   r!  r/   r   rc   rd   r  x_npr&  r   r  s   &&     rm   r  TestXP_Mean.test_dtype6%  s     hhrzz"&&zz3*BJJ7zz$ [[h''4.C''$-CJJ##C0CC1	 ( t::.jjD

!CDE! ('s   =A*EE+	c                    VP                  ^
4      pVP                  R4      p\        \        V4      \        V4      4       \        \        W2R7      \        W3R7      4       R# )rO   r   r
  N)r   r0   r!   r   s   &&  rm   test_integerTestXP_Mean.test_integerJ%  sB    IIbMIIcNXa[1.0FGrp   c                   \         P                  P                  R 4      pVP                  R4      w  r4rV\        VP	                  W4R,          ,           4      VP	                  WVR,          ,           4      R7      p\         P
                  ! W4R,          ,           WVR,          ,           R7      p\        WqP	                  V4      4       R# )r%  r  r
  N)r   r  )r   r  r  r!   rY   r7  r/   )	rc   rd   r  rf   rg   wxwyr   r  s	   &&       rm   r   TestXP_Mean.test_complex_gh22404Q%  s~    ii##N3zz'*brzz!d(+RZZU
5KLjjrT22:6ZZ_-rp   r   NrW   rU   )rZ  rE   )r   r   r   r   r   r   r  r(  r+  r   r.  r  r   r5  r  r  rD  r  r   r   r   s   @rm   r#  r#  $  s!    [[V%;<[[Yt5[[Z%7. 8 6 =. # [[ WX[[ VW1 X Y1 [[9""@ &	& '	&"" [[>"""H. .rp   r#  c                     a  ] tR tRt o ]P
                  P                  R. RO4      ]P
                  P                  RRR.4      ]P
                  P                  R^ ^.4      ]P
                  P                  RR	R
.4      R 4       4       4       4       tR tR t	]
! RR7      R 4       t]
! RR7      R 4       tR t]P
                  P                  R4      R 4       tR tR tRtV tR# )
TestXP_VariY%  r?   Nr  FTrs   r   r  r   c           	     $   \         P                  P                  R 4      pVP                  R4      p\         P                  pVR8X  dB   VP                  VP                  R7      R8  p	\         P
                  Wy&   \         P                  pVP                  V4      p
\        WW4VR7      p\        4       ;_uu_ 4       pVP                  \        R4       V! WrW4R7      pRRR4       \        WP                  X4      4       R#   + '       g   i     L,; i)	r%  r   r  r1   )r?   r  rs   r   r  )r?   r  rN  Nr  )r   r  r  r}   r  rb   nanvarrY   r"   r   r   r   r/   )rc   rd   r?   r  rs   r   r  rf   var_refnan_maskr&  r   r   r  s   &&&&&&        rm   test_xp_var_basicTestXP_Var.test_xp_var_basicZ%  s    
 ii##N3JJy!&&zzqwwz/#5H&&AKiiGzz!}d!+-   CJJ~'JK!KC ! 	ZZ_-	 ! s   :!C??D	c                    \        VP                  R R.4      ^R7      p\        W!P                  VP                  4      4       R# )r   r   rr   N)r"   rY   r/   rb   )rc   rd   r   s   && rm   r.  TestXP_Var.test_special_casess%  s0    bjj"b*q9ZZ/0rp   c                \   VP                  R 4      pV^8H  pVP                  W1P                  V4      p\        V4      p\        VRR7      pVP	                  VP                  4      p\        WF4       \        WV4       \        VRR7      pVP                  W#( ,          4      p\        Wv4       R# )r   r  r   r   N)r   rP  rb   r"   rY   r0   r}   r/   )rc   rd   rf   r  r  r  r  r   s   &&      rm   r  TestXP_Var.test_nan_policyx%  s    IIcNQHHT661% qzq[1jj "" aF+ffQuX!rp   r  c                ~   VP                  R 4      pVP                  V^8H  VP                  V4      pRp\        P                  ! \
        VR7      ;_uu_ 4        \        V\        P                  ,          RR7      pVP                  VP                  4      p\        WE4       RRR4       R#   + '       g   i     R# ; ir3  )
r   rP  rb   r   rb  r   r"   r   rY   r0   r4  s   &&    rm   r5   TestXP_Var.test_nan_policy_warns%  s~    IIcNHHQ!VRVVQ' +\\.88!bff*8C**RVV$CC% 9888r7  c           	         R p\         P                  ! \        VR7      ;_uu_ 4        \        VP	                  ^^VP
                  .4      RR7       RRR4       R#   + '       g   i     R# ; i)r   r   r   r   N)r   r   r   r"   rY   rb   r
  s   && rm   r   TestXP_Var.test_nan_policy_raise%  sF     2]]:W55BJJ1bff~.7C 6555s   *AA,	c                   R p\         P                  ! \        VR7      ;_uu_ 4        \        VP	                  . 4      4      pVP	                  VP
                  4      p\        W44       RRR4       Rp\         P                  ! \        VR7      ;_uu_ 4        \        VP	                  . .4      ^R7      pVP	                  VP
                  .4      p\        W44       RRR4       \        VP	                  . .4      ^ R7      pVP	                  . 4      p\        W44       R#   + '       g   i     L; i  + '       g   i     L^; ir9  )r   rb  r   r"   rY   rb   r0   r:  s   &&   rm   r  TestXP_Var.test_empty%  s    @\\,G<<"**R.)C**RVV$CC% =
 G\\,G<<"**bT*3C**bffX&CC% =
 bjj"&Q/jjn! =< =<r<  r=  c           	     t   VP                  VP                  4      P                  p\        P                  ! W"^,          .\        P                  R7      pVP	                  V4      p\        V4      p\        P                  ! V4      p\        P                  P                  V\        P                  4       \        WQP	                  V4      4       \        WAP                  R7      pVP	                  \        P                  ! \        P                  ! V\        P                  R7      4      4      p\        WV4       R# )rE   r6   N)r   r   r  r   rY   r"   r}   r"  r   r!  r/   r   r@  s   &&     rm   r  TestXP_Var.test_dtype%  s     hhrzz"&&zz3A,bjj9zz$dmffTl


RVV,ZZ_- d**-jj

4rzz BCD!rp   c                    VP                  ^
4      pVP                  R4      p\        \        V4      \        V4      4       R# )rO   r   N)r   r0   r"   r   s   &&  rm   rD  TestXP_Var.test_integer%  s.    IIbMIIcN
GAJ/rp   c                6   \         P                  P                  R 4      pVP                  R4      w  r4\        VP	                  W4R,          ,           4      4      p\         P
                  ! W4R,          ,           4      p\        WQP	                  V4      RR7       R# )r%  r  F)check_dtypeN)rE   r  )r   r  r  r"   rY   r}   r/   r  s   &&     rm   r  TestXP_Var.test_complex_gh22404%  se    ii##N3zz'"bjjrT*+ffQ2XZZ_%@rp   r   rJ  )r   r   r   r   r   r   r  rQ  r.  r  r   r5  r  r  r   r  rD  r  r   r   r   s   @rm   rL  rL  Y%  s     [[V%;<[[Z%7[[\Aq62[[\K+@A. B 3 8 =.*1
"" &	& '	& &D 'D"" [[>""0A Arp   rL  c           	      0   \         P                  P                  R 4      pVP                  RR7      pV P                  V4      p^p\	        W4V R7      w  rV\        WPP                  V4      4       \        Wd4       Rp\	        W4V R7      w  rV\        WPP                  VP                  4       4      4       \        V^ 4       ^p\	        VR,          W@R7      w  rV\        WPP                  \         P                  ! VR,          4      4      4       \        Wd4       R# )l   ~Mr  r
  Nr  r  )	r   r  r  rY   r   r0   r   r  
atleast_1d)rd   r  r  rf   r?   x_outaxis_outs   &      rm   test_chk_asarrayrh  %  s    
))


.C		#B


2AD"1B7OEE::b>* D"1B7OEE::bhhj121D"1W:D@OEE::bmmBwK&@AB rp   numpyz,These parameters *are* compatible with NumPyc                    V P                  . RO4      pRp\        P                  ! \        VR7      ;_uu_ 4        \        P
                  ! VRR7       RRR4       \        P                  ! \        VR7      ;_uu_ 4        \        P
                  ! VRR7       RRR4       R#   + '       g   i     LW; i  + '       g   i     R# ; i)	rW   r  r   r   r   NTr  r  )rY   r   r   r  r[   r  )rd   rf   r  s   &  rm   'test_axis_nan_policy_keepdims_nanpolicyrk  %  sw     	

< A5G	*'	:	:

1( 
;	*'	:	:

1t$ 
;	: 
;	:	:	:	:s   B"?B5"B2	5C	)	rW   rE   r   r   rw   rz   rJ   rF   rI   )	ry   ry   ry   ry   ry   ry   ry   ry   ry   )	iiiiiiiii)	g~?g<?gEk?g?ge(?gq?g?g8C?gG?)	g   mBg   }Bg  yӅBg   Bg  @0Bg  yӕBg  BwBg   Bg   ^B)	r  g-=gAfc=g-=gdy=gAfc=gYLɞ=g-=gSSʣ=)	r1   r2   rt   r  rA   rB   rC   rZ  r  )r   rF   rQ   rF   r   rH  gfx(@)rE   r-
  rQ   rE   r   r  g{T4@)r   rw   rJ   rI   r  r	  r  r	  r	  rn  r  )r5  r!  rp  r  r\  collectionsr   	itertoolsr   hypothesis.extra.numpyextrari  r  r  r  numpy.testingr   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   scipy.statsr[   scipy.stats.mstatsr{  scipy.stats._mstats_basic_mstats_basicr  scipy.stats._ksstatsr   scipy.special._testutilsr   scipy.specialr   scipyr   common_testsr   scipy.stats._axis_nan_policyr   r   r   r   r   r   r  r   r   r   r    r!   r"   r#   scipy._lib._utilr$   scipy.conftestr%   scipy._lib._array_apir&   r'   r(   r)   r*   r+   r,   r-   r.   scipy._lib._array_api_no_0dr/   r0   scipy._lib.array_api_extra_libarray_api_extrar_   lazy_xp_modulesr   r   r  rZ   r/  r   r   r   r   r  r4   r   r   r7  r  rt  r  r  r  r  r>	  r  r  r  r  r  r  r  r!  r  r  r  r  r  rH  rD  rY  rW  r  r  r  r  r  r  r  rj  rf  r  r  r  r  r  r  	compositer  r  r  r<  PowerDivCaser  r  r   r  r  r  r  r  r  r  r  r1  r  r  r  r  rB  r  r  r  r  r  r  r  r  r  r  r  r   r  r@	  r_	  r	  r	  r	  r	  r	  r	  r  r	  r	  r	  r	  r	  r
  r
  r
  r
  r%
  r8
  r7
  r=
  rL
  rJ
  rd
  r
  r
  r
  r
  r
  r
  r
  r
  r  r
  r
  r  r  rA  rr  r  r  r  r  r  r  ra  r  r  r  r  r  r  r%  rW  r~  r  r  r  rf   rg   wilcoxonr  rX  r  r3  r  r  r  r  r#  rL  rh  rk  r   rp   rm   <module>r     s   
  	  "  % %  . . .
  * / /   # # 0 0 ( -   -T TU U U & .G G G I ( (';;//  

u% %(  !&(	 238
:DeLDeL3U;KT KT\p# p#f 5>>"E> E> #E>PEL ELP{6 {6|~5 ~5VV:r4 < 3 3$TE TEnY2x	*&R+ +(n# n#b0D)3"rN rNjf3 f3R 599+E +E +E\ 5::j" j" j"Z 5<< f& f& !f&R 5==!0 0 "0*<@ <@~1f@ f@R 5<< e" e" !e"P1 1& 5::_" _" _"D 5>>"`"# `" #`"F    !< 5$$%J) J) &J)Zp> p>f & }Dqt"&&+266$<78AbffSkMAbffTlN:;I	K }N"&&+"&&,6266#;FGAbffSkMBrvvd|O;asmKL1	2 }AAD"&&+266$<78AbffSkMAbffTlN:;I	K |<aaQa1+ : r!!Qa1
 rxxBr
+--!!" rxxBr
+!!# 4 5))*A< A< +A<H 5??#(' (' $('V4Dn+( +(`Z. Z.~c. c.L	rEj1*+ ,88I.788I.79:0:0
. (HI J. ) ,,ryy}a.@A ??RYYr]BIIbM,JKMN5N5
/d 
/ 5??E$>$>?Q% @Q%h7At DEM7 M7 FM7`
 DEG5 G5 FG5TQ7 Q7h 5??#IB IB $IBXL$ 5??#y* y* $y*x 5--.) ) /), t4HIMNG O JG8% STRS5$$%9> & T U 9>x $'QR S, 5$$%k2RS% T &%: 5>>"N+ N+ #N+b*- *-Z 5>>"-> - #-6 5%%&-~ - '-B 5##$-^ - %- A A. 5$$%61 61 &61r{- {-|1"(>V+ +D ++)-+ DDD 5;;q3 q3  q3h 5;;n3 n3  n3b 5;;tW tW  tWn 5::R3 R3 R3j(.90[;|T7 T7n,/ ,/^i) i)X\) \)~X Xx 5(()b4 b4 *b4J#A #ALl  l ^[ [|@ @Fi iXHA HAV{1 {1| 	iiI&JJrNJJrN  >>A40 >>Auzz~~+>? >>Aq62 <<!Q011X+ X+vT. T.nJ. J.ZqA qAh!* '"PQ
% R
%rp   