
    (ph~                     h   S SK r S SKrS SKJr  S SKrS SKJr  S SK	J
r
  S SKrS SKJr  SSKJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJ r J!r!  S SK"J#r#  S SK$J%r%   S	r&\ RN                  S
:  r(1 Skr)1 Skr*1 Skr+1 Skr,1 Skr-1 Skr.SS1r/1 Skr01 Skr11 Skr21 Skr31 Skr4S1r5/ r6/ SQSS.r7SS// SQS.r8\Rr                  " \7\8/SS/5       HE  u  r:r;\Rx                  " St0 \:DS\;0D6r=\R|                  " \=\;S9r?\6R                  \?\A" 5       45        MG     S  rB\R                  R                  S!\B" 5       5      \R                  R                  S"S#/5      S$ 5       5       rES% rFS& rG\R                  R                  S'\F" 5       5      \R                  R                  S(S)/5      S* 5       5       rH\R                  R                  S!\B" 5       5      S+ 5       rIS, rJS- rK\R                  R                  \R                  R                  S.\K" 5       5      S/ 5       5       rM\R                  R                  S0\#5      S1 5       rN\R                  R                  S2/ S3Q5      S4 5       rOS5 rPS6 rQS7 rRS8 rSS9 rTS: rUS; rVS< rWS= rXS> rYS? rZS@ r[SA r\SB r]SC r^SD r_SE r`SF raSG rbSH rcSI rdSJ reSK rfSL rgSM rhSN riSO rjSP rk\R                  R                  SQ/ SRQ5      \R                  R                  SS\k" 5       5      ST 5       5       rlSU rmSV rnSW ro\R                  R                  SX 5       rp\R                  R                  SY 5       rrSZ rsS[ rtS\/ /S]S //S^S //S_S //S`S //SaS //SbS //ScS //SdS //SeS//Sf/ /Sg/ /Sh/ /Si/ /Sj/ /Sk/ //ruSlSm//Sn/ /SoSp///rv\R                  R                  Sq\u\v-   5      Sr 5       rwSs rxg)u    N)raises)IntegrationWarning)stats   )check_normalizationcheck_momentcheck_mean_expectcheck_var_expectcheck_skew_expectcheck_kurt_expectcheck_entropycheck_private_entropycheck_entropy_vect_scalecheck_edge_supportcheck_named_argscheck_random_state_propertycheck_meth_dtypecheck_ppf_dtypecheck_cmplx_derivcheck_picklingcheck_rvs_broadcastcheck_freezingcheck_munp_expect)distcont)rv_continuous_frozen   l        >
   ksonekstwokappa4vonmises
gausshypernorminvgaussrecipinvgaussvonmises_linerel_breitwignerstudentized_range>   pearson3crystalballpowerlognorm>   r   r   r   r    r#   r$   r&   >   r   genexpon	exponweib	johnsonsbtukeylambdar)   genhyperbolic>   ncfncx2r!   r#   r$   >   r   r   	irwinhall	trapezoidtruncparetolevy_stabler&   >   chi2exponlognormpowerlaw
loguniform
reciprocal>   betar0   argusexponpowgengammagompertzr,   	kstwobign	truncnormr!   
wrapcauchygeninvgausshalfgennormr"   genhalflogistictruncweibull_min>)   ftr/   nctburrfisklevyalphalomaxburr12cauchykappa3r   landaulevy_lmielkeparetobradfordinvgammar    	betaprimer+   	genparetor1   	jf_skew_t	johnsonsu	powernormr2   
foldcauchy
genextreme
halfcauchy
loglaplace
skewcauchy
truncexponr(   r3   r-   r)   r$   dpareto_lognormr%   >   r   r   r*   r4   r.   r#   r&   >8   rG   rH   chir/   rI   r;   r5   r0   ricer<   gammar   r   rdistrP   cosinedgammaerlangrR   rS   gennormmaxwelldweibullr>   rW   loggammalogisticnakagamir'   r8   skewnormr    rX   rY   r1   rZ   r,   r@   rA   r]   r!   r_   r9   r:   rC   rD   r-   halflogisticr"   r.   r$   rc   r%   rF   r&   rv_histogram_instance)r      rt      ru   ru      rv   rv   rv   r   r   r   r   r      rw   rw   rw      rx   rx      ry   	   ry   )abins)r   r   
   TFdensity)r~   c               #   D  #    [         S S  [        -    H  u  pU S:X  a  M  U [        ;   a1  [        R                  " X[        R
                  R                  S9v   MH  U [        ;   a1  [        R                  " X[        R
                  R                  S9v   M  X4v   M     g 7f)Nr4   marks)	r   histogram_test_instancesslow_test_cont_basicpytestparammarkslowxslow_test_cont_basicxslowdistnameargs     Z/var/www/html/venv/lib/python3.13/site-packages/scipy/stats/tests/test_continuous_basic.pycases_test_cont_basicr   n   sw     !!'??}$++,,xFKK4D4DEE..,,xFKK4E4EFF- @s   BB zdistname,argsni  c                 f    [        [        U 5      n[        R                  R                  S5      nUR                  " XUS.6nUR                  " U6 u  pgU S;  a  [        XgU5        [        X1U 5        [        X1U 5        [        X1U 5        [        X1U 5        [        X1U 5        [        X1U 5        [        X1U 5        [        X1U 5        [!        X1U 5        [#        X1U 5        SnU S:X  a  [%        UR&                  XU5        OU S:w  a  [%        XX5        Sn	UR(                  UR*                  UR&                  UR,                  UR.                  /n
SSS	S
SSS.nUR1                  U S5      nU S:X  a  SnOU S:X  a  Sn[3        X<XU
5        [5        X15        U S;   a"  [6        (       a  [8        R:                  " S5        O[=        X15        [?        X15        U S;  a  [A        X1U 5        URB                  S:X  a  [E        X15        URF                  RH                  [        RJ                  RH                  :w  a   U S:w  a  [M        X1[        RJ                  5        [N        RP                  " 5        nURS                  [T        S5        URS                  [T        S5        URS                  [V        S5        [Y        X15        S S S 5        [[        X15        []        X15        [_        X1U
5        [a        X15        U [b        ;  a  [e        X15        U S:w  a  [g        X1U 5        g g ! [         a    U nSn  GNf = f! , (       d  f       Ny= f)Nrs    sizerandom_state>   laplace_asymmetric{Gz?rC   r   r               ?g	@333333?      @)weibull_maxrS   rU   r3   r-   rs         ?
invweibullr   r   )ru   r%   fails on Linux 32-bit)r@   r   r/   r   r    z The occurrence of roundoff errorzExtremely bad integrandzinvalid valuerA   )4getattrr   	TypeErrornprandomRandomStatervscheck_sample_meanvar_check_cdf_ppfcheck_sf_isfcheck_cdf_sfcheck_ppf_isf	check_pdfcheck_pdf_logpdfcheck_pdf_logpdf_at_endpointscheck_cdf_logcdfcheck_sf_logsfcheck_ppf_broadcastcheck_distribution_rvscdfpdflogpdflogcdflogsfgetr   r   	_IS_32BITr   skipr   r   r   numargscheck_vecentropy	__class___entropyrv_continuousr   nptsuppress_warningsfilterr   RuntimeWarningr   check_retrieving_supportr   r   r   fails_cmplxr   check_ppf_private)r   r   r   distfnrngr   mvrM   locscale_defaultsmethsspec_xxsups                 r   test_cont_basicr   z   s   +)
 ))


'C
**s
5C<<DA--aC(&x(h'h'&x(f8$V(+!&x8V(+6)X.E**vzz3s;	]	" 	xe9ZZ

FMM\\E "TC'*,F 	

8S!A<	W	V>,&&99+,v#6 44f8,~~%!!U%8%8%A%AAJ&f5+>+>?				 C

%'IJ

%'@A

>?3 -	 
! V)v#V%(F {"&&;&x0 ]  +*+~ 
!	 s   L !AL"LL"
L0c               #     #    [         R                  R                  n [         R                  R                  n[         R                  R	                  SS9n[         R                  R	                  SS9n[
        S S  [        -    GHu  u  pES GHh  nS GH]  nUS:X  a$  U[        ;   a  [         R                  " XEXgU S9v   M.  US:X  a$  U[        ;   a  [         R                  " XEXgUS9v   MX  US:X  a$  U[        ;   a  [         R                  " XEXgUS9v   M  US:X  a$  U[        ;   a  [         R                  " XEXgUS9v   M  US:X  a$  U[        ;   a  [         R                  " XEXgU S9v   M  US:X  a%  U[        ;   a  [         R                  " XEXgUS9v   GM  US:X  a%  U[        ;   a  [         R                  " XEXgUS9v   GM,  US:X  a%  U[        ;   a  [         R                  " XEXgUS9v   GMW  XEXg4v   GM`     GMk     GMx     g 7f)	NzTest fails and may be slow.reasonz*Test too slow to run to completion (>10m).)MLEMM)TFr   r   r   )r   r   r   r   r   r   r   slow_fit_mler   xslow_fit_mlexfail_fit_mleskip_fit_mleslow_fit_mmxslow_fit_mmxfail_fit_mmskip_fit_mm)r   r   failr   r   r   methodfix_argss           r   cases_test_cont_basic_fitr      s    ;;DKKE;;#@AD;;#OPD!!'??#F)U?x<'? ,,xfdSSU?x='@ ,,xfeTTU?x='@ ,,xfdSSU?x<'? ,,xfdSST>h+&= ,,xfdSST>h,&> ,,xfeTTT>h,&> ,,xfdSST>h+&= ,,xfdSSV555 * $ @s   G:G<c                     [        [        R                  [        5      R                  [        5      5      [        [        5      [        [        5      -   [        [        5      -   :X  d   e[        [
        R                  [        5      R                  [        5      5      [        [
        5      [        [        5      -   [        [        5      -   :X  d   eg N)lenr   unionr   r   r   r   r        r   test_cont_basic_fit_casesr      s    ##M288FG]!33c,6GGH I H""<066{CDL 11C4DDE F Er   zdistname, arg, method, fix_argsn_fit_samples   c                      [        [        U 5      n[        R                  R                  S5      nUR                  " XUS.6nU(       a  [        XQXs5        g [        XQXs5        g ! [         a    U n N`f = f)Nr   r   )	r   r   r   r   r   r   r   check_fit_args_fixcheck_fit_args)r   r   r   r   r   r   r   r   s           r   test_cont_basic_fitr      sf    ) ))


'C
**#C
@C64vC0  s   A$ $A32A3c                 V    [        [        U 5      n[        R                  " UR
                  " U6 5      (       d   e[        R                  " UR
                  " USS065      (       d   e[        R                  " UR
                  " USS 065      (       d   eg ! [         a    U nSn  Nf = f)Nrs   r   r   )r   r   r   r   isscalarr   )r   r   r   s      r   test_rvs_scalarr     s    +)
 ;;vzz3'((((;;vzz30R01111;;vzz32T23333  +*+s   B B('B(c                  8    [        [        R                  S5        g )N)r   皙?)r   r   r4   r   r   r   &test_levy_stable_random_state_propertyr     s       1 1:>r   c               #     #    [        5       n S1nS1n[        S S  [        -    H  u  p4US:X  a  M  U[        ;   a8  [        R
                  " X4SSSS[        R                  R                  SS9S9v   MO  X0;  nX1;  nX2;  n[        5       n[        R
                  " X4XVUSUS9v   U(       a  U(       a	  U(       a  M  [        R
                  " X4SSSS[        R                  R                  /U-   S9v   M     g 7f)	Nr/   r[   r4   Ttoo slowr   r   F)
setr   r   xslow_test_momentsr   r   r   r   listxfail)	fail_normalizationfail_higherfail_momentr   r   cond1cond2cond3r   s	            r   cases_test_momentsr  #  s     'K-K!!'??}$)),,xdD$%+[[%6%6j%6%IK K2++ ll8% / 	/ E ,,xdD$&,kk&7&7%85%@B B9 @s   B3C59<C5z=distname,arg,normalization_ok,higher_ok,moment_ok,is_xfailingc           
          [        [        U 5      n[        R                  " 5        nUR                  [        S5        UR                  [        S5        UR                  [        S5        U(       a  UR                  [        5        UR                  " USS06u  pp[        R                  " SS9   U(       a  [        XaU 5        U(       a?  [        XaX5        [        XaXX5        [        XaXU 5        [        XaXX5        [        XaU 5        S S S 5        [        XaXU 5        U(       a  [!        XaXU 5        S S S 5        g ! [         a    U nSn  GN:f = f! , (       d  f       NM= f! , (       d  f       g = f)	Nrs   z9The integral is probably divergent, or slowly convergent.z#The maximum number of subdivisions.z The algorithm does not converge.momentsmvskignoreall)r   r   r   r   r   r   r   r   errstater   r	   r   r
   r   r   check_loc_scaler   )r   r   normalization_ok	higher_ok	moment_okis_xfailingr   r   r   r   sks               r   test_momentsr  H  s.   +)
 
			 C

%N	P

%8	:

%5	7 JJ)*\\377
a[[X&#F:!&q;!&qQA aH=!&qQA!&x8 ' 	Q84aH57 
!	 	  +*+" '& 
!	 s6   D; BE!/AE	)E!;EE
E	E!!
E/zdist,shape_argsc                 0   U S;   a  [         R                  " S5        U S;   a!  [        (       a  [         R                  " S5        U S;   n[        [        U 5      n[
        R                  " S5      n[
        R                  " S5      nUR                  n/ nSS/n[        U5       HQ  n	U	S	-   4S
U	S-   -  -   n
UR                  X   [
        R                  " U
5      -  5        UR                  SU	S	-   5        MS     UR                  XE/5        [        X0XxUS5        g )N)r!   r&   r   r   r   )r<   rX   ri   rc   rm   	exponnormr.   rC   rR   r4   rI   r"   re   rq   semicircularrk   rn   rt   )ru   r   ru   rv   r   r   d)r   r   r   r   r   r   zerosonesr   rangeappendinsertextendr   )dist
shape_args
shape_onlydistfunclocscalenargsallargsbshaper  shps              r   test_rvs_broadcastr&  r  s    22J""yy+,  M MJ
 ud#H
((1+CGGFOEEGVF5\1uhq1u%z}RWWS\12aQ  NNC<  SIr   zx,n,sf,cdf,pdf,rtol))gh㈵> ʚ;g$?gm%?g0eD@g+<)g&.!>r'  gי?gscl)D>g ^RUU!@vIh%,=)gMb@?r'  g_H'9$      ?gL.'r(  c                    [         R                  n[        R                  " UR	                  X5      UR                  X5      UR                  X5      /5      n[        R                  " X#U/5      n[        R                  " XxUS9  [        R                  " US   US   -   S5        [        R                  " UR                  X!5      /U /SS9  g )Nrtolr   r   r)  :0yE>)r   r   r   arraysfr   r   r   assert_allcloseassert_equalisf)	r   nr/  r   r   r,  ksvalsexpecteds	            r   test_gh17775_regressionr7    s    $ 
B88RUU1["&&,q=>Dxx#'HT2T!WtAw&,!48r   c                     [         R                  R                  S5      n [        R                  R                  [         R                  " S5      SU S9n[         R                  " U5      n[        R                  " [         R                  " US:g  5      S5        [        R                  R                  S[         R                  " S5      U S9n[         R                  " U5      n[        R                  " [         R                  " US:g  5      S5        [        R                  R                  [         R                  " S5      [         R                  " S5      U S9n[         R                  " U5      n[        R                  " [         R                  " US:g  5      S5        [        R                  R                  [         R                  " S/S//5      [         R                  " S5      U S9n[         R                  " UR                  5       5      n[        R                  " [         R                  " US:g  5      S5        [        [        [        R                  R
                  SS/SS//SS/SS//S5        [        [        [        R                   R
                  / SQSSS5        [        [        [        R                   R
                  / S	Q/ S
QS/S//S5        g )N{   r   r   )r   r!  r   r   z0All the values are equal, but they shouldn't be!)rt   ru   rv   r   )rt   rt   )r   r   r   r   )r   r   r   r   rt   )rv   )r   r   r   r   normr   r  diffr   assert_r  r  r.  ravelassert_raises
ValueErrorrf   )r   r5  r  s      r   test_rvs_gh2069_regressionr@    s    ))


$C::>>bhhqk>ED
AKKqAv RS::>>arwwqz>DD
AKKqAv RS::>>bhhqk#>ND
AKKqAv RS::>>bhhaSz2"''!*'*  ,D


AKKqAv RS*ejjnn1v1v.>q6Aq6"A'*ekkoo|Q6J*ekkoo|\3*d$r   c                     [         R                  n [        R                  " U R	                  SS[
        R                  5      S5        [        R                  " U R                  S/S/[
        R                  /5      S5        [        R                  " U R	                  S[
        R                  * S5      S5        [        R                  " U R                  S/[
        R                  * /S/5      S5        [        R                  " U R                  S/S/[
        R                  /5      S5        [        R                  " U R	                  SS[
        R                  5      S5        [        R                  " U R                  S/[
        R                  * /S/5      S5        [        R                  " U R	                  S[
        R                  * S5      S5        [        R                  " U R	                  S[
        R                  * S5      S5        g )Nr   r   gA?g|N?)r   rA   r   assert_almost_equalr   r   inf_cdf)tns    r   test_nomodify_gh9900_regressionrG    s{    
B BFF1a0.0BGGQC!rvvh7.0 BFF2w2/1BGGRDBFF7)aS9/1 BGGQC!rvvh7.0BFF1a0.0 BGGRDBFF7)aS9/1BFF1rvvgq1BFF2w2/1r   c            	      $   [         R                  " / SQ5      n [         R                  " / SQ5      n[        X5       VVs/ s H%  u  p#[        R                  R                  SX#5      PM'     nnn[        R                  " [        R                  R                  SX5      U5        [        X5       VVs/ s H%  u  p#[        R                  R                  SX#5      PM'     nnn[        R                  " [        R                  R                  SX5      U5        [        X5       VVs/ s H%  u  p#[        R                  R                  X"U5      PM'     nnn[        R                  " [        R                  R                  X U5      U5        [        X5       VVs/ s H%  u  p#[        R                  R                  X2U5      PM'     nnn[        R                  " [        R                  R                  XU5      U5        g s  snnf s  snnf s  snnf s  snnf )N)r   rt   ru   rv   r   rw   )ry      r       r   0   rx   r   )r   r.  zipr   r:   r   r   assert_array_almost_equal)r{   b_a_banss        r    test_broadcast_gh9990_regressionrR    sz    	#$A
&'A9<Q
Bvr52*C
B!!%"2"2"6"6q!"?E9<Q
Bvr52*C
B!!%"2"2"6"6q!"?E:=a(
C(5+(C
C!!%"2"2"6"6qQ"?E:=a(
C(5+(C
C!!%"2"2"6"6qQ"?E C C D Ds   ,G:1,H #,H,Hc            	          [         R                  R                  [        R                  " / SQ5      S[        R                  " / SQ5      -
  S-  [        R
                  [        R                  " / SQ5      SS9  g )N)      @       @r)  r   )g      @r   g      @rT  )r{   rN  r   r!  )r   rA   r   r   r.  rD  r   r   r    test_broadcast_gh7933_regressionrV    sQ    	OO
!/**c
1
&&HH_%  r   c            	         [         R                  SSS2   n [         R                  [         R                  " S5      * [         R                  " S5      4   n[        X5       VVs/ s H3  u  p#[        R
                  R                  X#[         R                  5      PM5     nnn[        R
                  R                  X[         R                  5      n[        R                  " XT5        g s  snnf )Nrt   y             @Y@2   3   )
r   r_r  rL  r   rA   r   rD  r   rM  )r   r{   _xrO  r6  rQ  s         r   test_gh2002_regressionr]  &  s     	b4iA
rwwr{lBGGBK'(ABEa)L)##BBFF3)HL
//

aBFF
+C!!#0 Ms   #:C%c                  ~    Sn [         R                  R                  S[        R                  " U /U S-   //5      5        g )Ng(\@r   )r   r^   ppfr   r.  )cs    r   test_gh1320_regressionra  0  s3    A	bhha#gY'789r   c                     [         R                  R                  S5        / SQn SS[         R                  " S5      -  S-  -
  nSS[         R                  " S5      -  S-  -   n[        [        [        R                  5      [        R                  ]#  U SS9u  p4[        R                  " X1S	S
9  [        R                  " X4-   US	S
9  g )Ni  )r   r   r   r   r   皙?rt   ru   r   r   r   rv   )decimal)r   r   seedsqrtsupertyper   uniformfitr   rC  )r   r{   rN  r   r!  s        r   test_method_of_momentsrl  <  s    IINN4Aa
l1nAa
l1nAtEMM*EMM>q>NJCCA.CIq!4r   c                     [         R                  " U 5      (       a  [        X 5        [         R                  " U5      (       a  [        X!5        g g r   )r   isfinitecheck_sample_meancheck_sample_var)popmeanpopvarsamples      r   r   r   H  s5    	{{7&*	{{6( r   c                 T    [         R                  " X5      R                  nUS:  d   eg )Nr   )r   ttest_1samppvalue)rs  rq  probs      r   ro  ro  O  s$    V-44D$;;r   c                     [         R                  " U 4S SS9nUR                  nUR                  UR                  pTXAs=::  a  U::  d   e   eg )Nc                 "    U R                  SUS9$ )Nr   )ddofaxis)var)r   r{  s     r   <lambda>"check_sample_var.<locals>.<lambda>[  s    140r   gףp=
?)confidence_level)r   	bootstrapconfidence_intervallowhigh)rs  rr  resconfr  r  s         r   rp  rp  U  sP     //		0C
 ""D$)) D     r   c                     / SQn[         R                  " U R                  " U R                  " U/UQ76 /UQ76 U[        US-   S9  g )N)gMbP?r   g+?z - cdf-ppf roundtripre  err_msg)r   rC  r   r_  DECIMAL)r   r   msgvaluess       r   r   r   c  sB     FFJJvzz&'?3'?F#F"GS2>34r   c                     [         R                  " U R                  " U R                  " / SQ/UQ76 /UQ76 / SQ[        US-   S9  g )Nr   r   ?z - sf-isf roundtripr  )r   rC  r/  r2  r  r   r   r  s      r   r   r   j  s>    FIIfjj&G3&GN#N+Wc1G23r   c                     [         R                  " U R                  " SS//UQ76 SU R                  " SS//UQ76 -
  [        US-   S9  g )Nr   r  r)  z - cdf-sf relationshipr  )r   rC  r   r/  r  r  s      r   r   r   p  sK    FJJSz8C8&))S#J"="==$+S4656r   c                     [         R                  " SS/5      n[        R                  " U R                  " U/UQ76 U R
                  " SU-
  /UQ76 [        US-   S9  g )Nr   r  r   z - ppf-isf relationshipr  )r   r.  r   rC  r2  r_  r  )r   r   r  ps       r   r   r   w  sS    
#sAFJJq/3/AaC1F#1F$+S5667r   c                 <   U R                   " S/UQ76 nSnU R                  " U/UQ76 nUS:  d  US:  a  US-   nU R                  " U/UQ76 nU R                  " X4-   /UQ76 U R                  " X4-
  /UQ76 -
  U-  S-  nUS-  n[        R                  " XV[
        US9  g )	Nr   gư>g-C6?     @r   rU  z - cdf-pdf relationshipr  )r_  r   r   r   rC  r  )r   r   r  medianepspdfvcdfdiffs          r   r   r   ~  s    ZZ"c"F
C::f#s#Dt #zz&'3'zz&,--zz&,--./23367G $$CD7CHr   c                    [         R                  " / SQ5      nU R                  " U/UQ76 nU[         R                  " U5         nU R                  " U/UQ76 nU R
                  " U/UQ76 nXUS:g  [         R                  " U5      -     nU[         R                  " U5         nUS-  n[        R                  " [         R                  " U5      USUS9  g )N)rc  r   皙?r   333333?ffffff?皙?r    - logpdf-log(pdf) relationshiprx   r  	r   r.  r_  rn  r   r   r   rC  logr   argsr  pointsr5  r   r   s          r   r   r     s    XX9:F::f$t$DD!"D
**T
!D
!C]]4'$'F
ax2;;s++
,CBKK'(F,,CBFF3KCHr   c                    [         R                  " SS/5      nU R                  " U/UQ76 nU[         R                  " U5         nU R                  " U/UQ76 nU R
                  " U/UQ76 nXUS:g  [         R                  " U5      -     nU[         R                  " U5         nUS-  n[        R                  " [         R                  " U5      USUS9  g )Nr   r   r  rx   r  r  r  s          r   r   r     s    XXq!fF::f$t$DD!"D
**T
!D
!C]]4'$'F
ax2;;s++
,CBKK'(F,,CBFF3KCHr   c                 x   [         R                  " / SQ5      nU R                  " U/UQ76 nU[         R                  " U5         nU R                  " U/UQ76 nU R
                  " U/UQ76 nXUS:g     nU[         R                  " U5         nUS-  n[        R                  " [         R                  " U5      USUS9  g )N)	        rc  r   r  r   r  r  r  r)  r   z - logsf-log(sf) relationshiprx   r  )	r   r.  r_  rn  r/  r   r   rC  r  )r   r  r  r  r5  r/  r   s          r   r   r     s    XXCDF::f$t$DD!"D	4	$	BLL%%E	!GB"++e$%E**CBFF2Jq#Fr   c                 x   [         R                  " / SQ5      nU R                  " U/UQ76 nU[         R                  " U5         nU R                  " U/UQ76 nU R
                  " U/UQ76 nXUS:g     nU[         R                  " U5         nUS-  n[        R                  " [         R                  " U5      USUS9  g )N)	r   rc  r   r  r   r  r  r  r)  r   z - logcdf-log(cdf) relationshiprx   r  )	r   r.  r_  rn  r   r   r   rC  r  )r   r  r  r  r5  r   r   s          r   r   r     s    XXABF::f$t$DD!"D
**T
!D
!C]]4'$'F
Qh-CBKK'(F,,CBFF3KCHr   c                    Sn/ U-  nU(       a*  U Vs/ s H  n[         R                  " U/U-  5      PM     nnU R                  " S/UQ76 nU R                  " S/UQ76 nUS-  n[        R                  " Xv/U-  SUS9  g s  snf )Nr   r   z - ppf multiplerx   r  )r   r.  r_  r   rC  )r   r   r  num_repeatsr  _r  medianss           r   r   r     s    KD
589S!{*+S9ZZ"c"Fjj$t$GCGX%;QPST :s   $A?c                    [         R                  " X0USS9u  pEXR:  ak  [         R                  " X USS9u  pE[        R                  " XR:  S[	        U5      -   S-   [	        U5      -   S-   [	        U5      -   S-   [	        U5      -   5        g g )Ni  )r  NzD = z	; pval = z
; alpha = z
args = )r   kstestr   r<  str)r  r  rM   r   Dpvals         r   r   r     s     ll3448GA ,,t=DL&3q6/K"?#d)"K #!#&u:#.0;#<>A$i#H 	I 	r   c                 f    [         R                  " U R                  " U6 U R                  " U6 5        g r   )r   r1  
vecentropyr   )r   r  s     r   r   r     s&    V&&-v/EFr   c                     [         R                  " SS/5      [         R                  " SS/5      peU R                  " XUS.6u  px[        R                  " X&-  U-   U5        [        R                  " X6-  U-  U5        g )N      $@g      4@r   r!  )r   r.  r   r   r0  )	r   r   r   r   r  r   r!  mtvts	            r   r
  r
    sc     4,'4,)?\\3u5FB#r*r*r   c                     U R                   " [        R                  " / SQ5      /UQ76 n[        R                  " [        R
                  " [        R                  " U5      5      (       + US-   5        g )Nr  zppf private is nan)_ppfr   r.  r   r<  anyisnan)r   r   r  ppfss       r   r   r     sF    ;;rxx0737DKKBFF288D>**C2F,FGr   c                     Su  p#U R                   " U6 nU R                   " XUS.6n[        R                  " [        R                  " U5      U-  U-   [        R                  " U5      5        g )N)r   rt   r  )supportr   rC  r   r.  )r   r  r   r!  suppsupp_loc_scales         r   r   r     sU    JC>>4 D^^T%@NBHHTN5036HH^46r   c                    [         R                  " SS9   [        R                  " 5        nUR	                  [
        SS9  UR	                  [
        SS9  U R                  X#S9nU R                  USUS9nS S S 5        S S S 5        [        R                  " [        W5      S	[        U5      -   :H  5        [        R                  " [        W5      S	[        U5      -   :H  5        g ! , (       d  f       Ns= f! , (       d  f       N|= f)
Nr  r  !The shape parameter of the erlangcategorymessagezfloating point number truncatedrd  powell)	optimizerr   rt   	r   r	  r   r   r   r   rk  r<  r   )r   r   r   r   r   r5  vals2s          r   r   r     s    		"C$9$9$;s

N> 	 	@

N< 	 	>zz#z-

3(6
B %<	" KKD	Qs3xZ'(KKE
aCj() %<$;	"	"s#   C2A	C!4C2!
C/	+C22
D c           	         [         R                  " SS9   [        R                  " 5        nUR	                  [
        SS9  U R                  USUS9nU R                  USUS9n[        R                  " [        U5      S	[        U5      -   :H  5        [        R                  " US
   S:H  5        [        R                  " US   S:H  5        [        R                  " [        U5      S	[        U5      -   :H  5        [        U5      S:  a`  U R                  X!S   US9n[        R                  " [        U5      S	[        U5      -   :H  5        [        R                  " US   US   :H  5        [        U5      S:  a`  U R                  X!S   US9n[        R                  " [        U5      S	[        U5      -   :H  5        [        R                  " US   US   :H  5        [        U5      S	:  a`  U R                  X!S	   US9n	[        R                  " [        U	5      S	[        U5      -   :H  5        [        R                  " U	S	   US	   :H  5        S S S 5        S S S 5        g ! , (       d  f       N= f! , (       d  f       g = f)Nr  r  r  r  r   )flocr   r   )fscaler   rt   rX  rB  )f0r   )f1r   )f2r   r  )
r   r   r   r   r   r5  r  vals3vals4vals5s
             r   r   r     s   		"C$9$9$;s

N> 	 	@ zz#Afz5

3q
8CI3s8+,DHM"E"IN#CJ!CH*,-s8a<JJs1vfJ=EKKE
aCj01KKaCF*+s8a<JJs1vfJ=EKKE
aCj01KKaCF*+s8a<JJs1vfJ=EKKE
aCj01KKaCF*++ %<	"	"$;$;	"	"s#   I%HII%
I"	I%%
I3c               #      #    [          HE  u  pU [        ;   a1  [        R                  " X[        R                  R
                  S9v   M@  X4v   MG     g 7f)Nr   )r   slow_with_listsr   r   r   r   r   s     r   cases_test_methods_with_listsr  %  s<     !&,,xFKK4D4DEE-	 "s   AAr   )r   r   r   r   r/  r   r_  r2  zdistname, argsc           	      Z   [        [        U5      n[        X05      nUS:X  a  U R                  S5      (       a  SS/nOSS/nU Vs/ s H  of/S-  PM
     nnSS/nSS	/n	U" U/UQ7XS
.6n
[        R                  " U
[        U/UQUPU	P76  Vs/ s H  o" U6 PM	     snSSS9  g s  snf s  snf )Nr   r  r   rt   r   rc  r   r   g)\(?r  g+=r(  )r,  atol)r   r   
startswithr   r0  rL  )r   r   r  r  rG   r   r{   shape2r   r!  resultr   s               r   test_methods_with_listsr  -  s     5(#DA<F$5$5e$<$<!H#J!"Tc!eTF"c(CIEq060s0F(+A(C(C(CU(CD(C1A(CD"0	 #
 Es   B#B(
c                      [         R                  R                  SSS5      n [        U [        5      (       d   e[         R
                  R                  SS5      n[        U[        5      (       d   eg )Nr   r   rv   ry   )r   rJ   moment
isinstancefloatrK   )vals0vals1s     r   (test_burr_fisk_moment_gh13234_regressionr  C  sV    JJaA&EeU####JJa#EeU####r   c            
          [         R                  R                  S[        R                  " / SQ5      SS9n [        R                  " / SQ5      n[
        R                  " X5        [         R                  R                  S[        R                  " / SQ5      SS9n[        R                  " [        R                  [        R                  [        R                  /5      n[
        R                  " X#5        [         R                  R                  S[        R                  " / SQ5      / SQS9n[        R                  " [        R                  S[        R                  /5      n[
        R                  " XE5        [         R                  R                  SS	S
S9n[        R                  n[
        R                  " Xg5        [        XgR                  5      (       d   e[         R                  R                  S/ SQ/ SQS9n[        R                  " S[        R                  [        R                  /5      n	[
        R                  " X5        [         R                  R                  S/ SQ/ SQS9n
[        R                  " S[        R                  S/5      n[
        R                  " X5        [         R                  R                  S/ SQ/ SQS9n[        R                  " [        R                  [        R                  [        R                  /5      n[
        R                  " X5        [         R                  R                  SSS	S	S9n[        R                  n[
        R                  " X5        [        XR                  5      (       d   e[         R                  R                  S/ SQS	S	S9n[        R                  " [        R                  [        R                  [        R                  /5      n[
        R                  " UU5        [         R                  R                  S/ SQ/ SQ/ SQS9n[        R                  " S[        R                  [        R                  /5      n[
        R                  " UUSS9  [         R                  R                  SSS/SS/5      n[        R                  " SS/5      n[
        R                  " UUSS9  SS	SS[        R                  /nSS	SS[        R                  /nSS	[        R                  " S5      /nS S	SS[        R                  /n[        R                  " U5      R                  S!5      n[        R                  " U5      R                  S"5      n[        R                  " U5      R                  S#5      n[        R                  " U5      n[         R                  R                  SUUUUS$9n[        R                   " UUUU5      u  nnnn[        R"                  " U5       Hv  n[        R$                  " S%S%S&9   US	   n[         R                  R                  SUU   UU   UU   UU   S$9n[        R&                  R                  UU   U5        S S S 5        Mx     g ! , (       d  f       M  = f)'Nr   r   rt   ru   orderr   r!  r)  rU  rT  rB  )r   r   rU  rt   r   )r   r   rt   )ru   r  r  )r   r   r   )r   rX  g      Y@g      9@r  )g      rX  g      Yr  dfr   r!  )r)  r  rU  )r)  g      r  g ﲙ"@r-  r+  r   r)  g      :@g      @gvIh%<=gg@g )rB  r   r   r   )rB  r   r   )rB  r   )r  r{   rN  r   r!  r  )invaliddivide)r   r:  r  r   r.  r   r1  nanr  r   rd   r0  pirg  reshaper;   broadcast_arraysndenumerater	  testing)r  	expected0r  	expected1r  	expected2r  	expected3r  	expected4r  	expected5vals6	expected6vals7	expected7vals8	expected8vals9	expected9vals10
expected10r{   rN  r   r!  vals11ir6  s                                r   *test_moments_with_array_gh12192_regressionr  K  s   JJA288I+>aHE&IU& JJA288I+>bIE"&&"&&"&&12IU& JJA288I+>$.  0E"&&"bff-.IU& JJA1B7EIU&e001111 JJA9KHE#rvvrvv./IU& JJA9NKE#rvvv./IU& JJA9<LME"&&"&&"&&12IU& II1;EIU&e001111 II1CE"&&"&&"&&12IUI& II1#0  2E*bffbff56Iyt4 ZZq2r(RH5F3+&J
7 
q!S"%% A	q!S"%% ABGGAJ
C1abee$E
M*A
J'A
((3-


(CHHUOEZZQ!qcGF**1ae<Aq#u^^A[[(;!Azz((qAaDAaD-0V58 ) EHJJ##F1Ix8 <; ;;s   AY..
Y=	c                     [         R                  R                  S[        R                  " / SQ5      S//S9n [        R                  " / SQ/5      n[
        R                  " X5        U R                  UR                  :X  d   e[         R                  R                  S[        R                  " S/S/S//5      / SQS9n[        R                  " / SQ/ SQ/ S	Q/5      n[
        R                  " X#5        UR                  UR                  :X  d   e[         R                  R                  S/ SQS
SS9n[        R                  " / SQ5      n[
        R                  " XESS9  UR                  UR                  :X  d   e[         R                  R                  SS/S/S/// SQ/ SQS9n[        R                  " [        R                  [        R                  S/[        R                  [        R                  S/[        R                  [        R                  S//5      n[
        R                  " XgSS9  UR                  UR                  :X  d   eg )Nr   r  r  r  rt   ru   )r)  r)  r)  )rU  rU  rU  )rT  rT  rT  r  r)  r  )g e3E?g> ?g e3E?r-  r+  rU  rT  )r  r)  rU  )g      r  rT  g@3F@gw,W.
@gf3&@)r   r:  r  r   r.  r   r1  shaperd   r0  r  )r  r  r  r  r  r  r  r  s           r   /test_broadcasting_in_moments_gh12192_regressionr    s   JJA288I+>seLE,(IU&;;)//)))JJA288aS1#sO+D$-  /E,lCDIU&;;)//)))II12RHE=>It4;;)//)))II12$rd);#0  2E266266:666266:666266:68 9I t4;;)//)))r   c                  \   / SQn Sn[         R                  " U VVs/ s H0  o  Vs/ s H   n[        R                  R                  X2S9PM"     snPM2     snn5      n[         R                  " [        R                  R                  XS95      n[        R
                  " XE5        g s  snf s  snnf )N)r   r         @      @      @r  r  )r   r.  r   rQ   r   r0  )shapesr  r  r
  r  res2s         r   test_kappa3_array_gh13582r    s     'FG
((6=?6=F( &u \\'''> &(6=? @C88ELL&&v&?@D"( ?s   	B(
'B#B(
#B(
c                     [         R                  " / SQ5      n [         R                  " / SQ5      nSn[         R                  " U VVs/ s H@  n[        S5       Vs/ s H&  n[        R                  R                  X   X   US9PM(     snPMB     snn5      n[         R                  " [        R                  R                  XUS95      n[
        R                  " XV5        [         R                  " / SQ5      n [         R                  " / SQ5      n[         R                  " U VVs/ s H@  n[        S5       Vs/ s H&  n[        R                  R                  X   X   US9PM(     snPMB     snn5      n[         R                  " [        R                  R                  XUS95      n[
        R                  " XV5        [         R                  " / S	Q5      n [         R                  " / S
Q5      S S 2S 4   n[         R                  " [        R                  R                  XUS95      nUR                  S:X  d   eg s  snf s  snnf s  snf s  snnf )N)r   r  r  r  r  )r   r   g      r   r  r  r   r  )rB        пr  r   rB  r   )r   r   r   gUUUUUUտrB  r   rw   )rB  r   r   )rB  r   r   r   )rv   rv   ru   )r   r.  r  r   r   r   r0  r
  )hr  r  r  r  r  r  s          r   test_kappa4_array_gh13582r    s   
*+A
()AG
((4;=4;&E!H&$q \\''adF'C$&4;= >C88ELL&&qW&=>D" 	+,A
)*A
((4;=4;&E!H&$q \\''adF'C$&4;= >C88ELL&&qW&=>D" 	A
!"1d7+A88ELL&&qW&=>D::"""#& =& =s0   H<
-H7H<
$I
7-I$I
7H<
I
c                     Sn [         R                  " [        U S9   [        R                  " 5       R
                    S S S 5        [         R                  " [        U S9   [        R                  " 5       R                    S S S 5        S[        R                  l        [        R                  " 5       n[        U[        5      (       d   e[        [        R                  S5        g ! , (       d  f       N= f! , (       d  f       N{= f)Nz.'rv_continuous_frozen' object has no attribute)matchherringpmf)
r   r   AttributeErrorr   r:  r  logpmfr  r   delattr)r  frozen_norms     r   test_frozen_attributesr     s     ?G	~W	5

 
6	~W	5

 
6EJJN**,Kk#78888EJJ 
6	5	5	5s    C! C2!
C/2
D c                     [         R                  R                  S5      n [         R                  * Sp![        R
                  " [        R                  R                  X5      [        R                  R                  U5      5        U R                  SS9U R                  SS9p!U R                  SS9S:  nSX#'   X   n[        R                  R                  X5      n[        R
                  " XS   [        R                  R                  U5      5        [        R
                  " XS)    [        R                  R                  X)    X#)    5      5        g )Nr   )ru   ru   )r   r   )
r   r   default_rngrD  r   r1  r   rq   r   r:  )r   r   r{   maskx_normr  s         r   test_skewnorm_pdf_gh16038r%    s    
))


"CFF7AqU^^''-uzz~~a/@A::6:"CJJFJ$;q::6:"S(DAGWF
..

Q
"CSY

v 67SZ!3!3AeHah!GHr   r   r   r   r   r   r/  r   r_  r2  r  entropyexpectr  meanstdr|  intervalgffffff?r  r   mvcasec                 <   U u  p[        [        R                  " 5       U5      nU" U6 nU [        ;   a"  [	        U[
        R                  5      (       d   eg [	        US   [
        R                  5      (       d   e[	        US   [
        R                  5      (       d   eg )Nr   r   )r   r   r:  
scalar_outr  r   number)r,  method_namer  r   r  s        r   test_scalar_for_scalarr1     s|     KUZZ\;/F
$-Cz#ryy))))#a&")),,,,#a&")),,,,r   c                  .   [         R                  R                  / SQ5      n [        U S   [        R
                  5      (       d   e[        U S   [        R
                  5      (       d   e[         R                  R                  / SQ5      n [        U S   [        R
                  5      (       d   e[        U S   [        R
                  5      (       d   e[         R                  R                  S/ SQ5      n [        U [        R
                  5      (       d   eg )Nr  r   r   r   )r   r:  rk  r  r   r/  fit_loc_scalennlf)r  s    r   test_scalar_for_scalar2r5    s    
**..
#Cc!fbii((((c!fbii((((
**
"
"9
-Cc!fbii((((c!fbii((((
**//&)
,Cc299%%%%r   r   )ysysnumpyr   numpy.testingr  r   r   r   r>  scipy.integrater   	itertoolsscipyr   common_testsr   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   scipy.stats._distr_paramsr   !scipy.stats._distn_infrastructurer   r  maxsizer   r   r   r   r   r   r   r   r   r   r   r   r   r  r   case1case2productr,  r~   	histogram_histrv_histogram_rv_histr  tupler   r   parametrizer   r   r   r   r   r   r  r   r  r&  r7  r@  rG  rR  rV  r]  ra  rl  r   ro  rp  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.  scalars_outr1  r5  r   r   r   <module>rJ     s   
    * .  
? 
? 
? 
? 
? 
? / B	 [[5 	<  C : 9OK23R2<5? ''  *34	6!fj)&&u~e}EMD'LL1411E!!%9H##Xuw$78 F	  )>)@Au%R1 & BR1j"6JF :2463%01 161 )>)@A
4 B
4?"BJ  '+-/#6/ #6L *H5&J 6&Jj .?	@9	@9$$:!1HF,1:	5)!4367I$
I
I
G
I
UI&G+H6
*,2   $A B)+H+JK0 LB0&$Q9h*4 # # # #0
I bkEA3<(QC51#,!oqc{WqcNUQCLqclXsOi_xnnvrlUBK%F
 TF#i_w6GH k!9:
- ;
-	&r   