
    \hL                        S SK Jr  S SKJrJrJr  S SKJr  S SKJ	r	  S SK
JrJrJrJr  S SKJrJr  S SKJr  S SKJrJrJr  S S	KJrJr  S S
KJrJrJrJ r   S SK!J"r"J#r#  S SK$J%r%J&r&  S SK'J(r(  S SK)J*r*  S SK+J,r,  S SK-J.r.J/r/J0r0J1r1J2r2  S SK3J4r4J5r5J6r6  S SK7J8r8  S SK9J:r:J;r;J<r<J=r=  S SK>J?r?J@r@JArA  S SKBJCrC  S SKDJErE  S SKFJGrG  S SKHJIrIJJrJ  S SKKJLrL  S SKMJNrN  S SKOJPrP  S SK9JQrQ  S SKDJRrR  S SKKJSrSJTrTJUrU  S SKVJWrWJrJXrXJYrYJZrZJ[r[J\r\J]r]J^r^J_r_J`r`JaraJbrbJcrcJdrdJereJfrfJgrgJhrhJiriJjrjJkrkJlrlJmrmJnrnJoroJprpJqrqJrrrJsrsJtrtJuruJvrvJwrwJxrxJyryJzrzJ{r{J|r|J}r}J~r~JrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJr  S S KJrJrJr  S S!KJrJr  S S"KJrJr  S S#KJr  S S$KJr  S S%KJrJrJrJr  S S&KJr  \GRl                  r\" \S'5      u  rrrS( rS) rS* rS+ rS, rS- rS. rS/ rS0 rS1 rS2 rS3 rS4 rS5 rS6 rS7 rS8 rS9 rS: rS; rS< rS= rS> r\S? 5       rS@ rSA rSB rSC r\SD 5       rSE rSF rSG rSH rSI rSJ rSK rSL rSM rSN rSO rSP rSQ r\SR 5       rSS rST rSU rSV rSW rSX rSY rSZ rS[ rS\ rS] rS^ rS_ rS` r\\Sa 5       5       rSb rSc rSd rSe rSf rSg rSh rSi rSj rSk rSl Gr Sm GrSn GrSo GrSp GrSq Gr\Sr 5       GrSs GrSt GrSu Gr	Sv Gr
Sw GrSx GrSy GrSz GrS{ GrS| GrS} Grg~)    )Sum)Lambdadiffexpand_func)Mul)
EulerGamma)EIRationalpi)EqNe)S)DummySymbolsymbols)binomial	factorial)Absimresign)explog)coshsinh)floor)sqrt)	Piecewise)asinatancossintan)besselibesseljbesselk)beta)erferfcerfiexpint)gamma
lowergamma
uppergamma)zeta)hyper)Integral)AndOr)Interval)simplify)lambdify)erfinvmeijerg)	FiniteSet
ComplementIntersection)JPr	   wheredensityvariance
covarianceskewnesskurtosismediangivenpspacecdfcharacteristic_functionmoment_generating_functionContinuousRVArcsinBeniniBetaBetaNoncentral	BetaPrimeCauchyChi
ChiSquaredChiNoncentralDagumDavisErlang
ExGaussianExponentialExponentialPowerFDistributionFisherZFrechetGammaGammaInverseGompertzGumbelKumaraswamyLaplaceLevyLogistic	LogCauchyLogLogisticLogitNormal	LogNormalMaxwellMoyalNakagamiNormalGaussianInverseParetoPowerFunction
QuadraticURaisedCosineRayleigh
ReciprocalShiftedGompertzStudentTTrapezoidal
TriangularUniform
UniformSumVonMisesWeibull
coskewnessWignerSemicircleWaldcorrelationmomentcmomentsmomentquantileLomaxBoundedPareto)NormalDistributionExponentialDistributionContinuousDistributionHandmade)MultivariateLaplaceDistributionMultivariateNormalDistribution)SingleContinuousPSpaceSingleContinuousDomain)CompoundPSpace)Probability)raisesXFAILslowignore_warnings)verify_numericallyxyzc                     [        SSS9n [        SSS9n[        SSS5      nX!-  U -   n[        U5      U :X  d   e[        U5      US	-  :X  d   e[	        U5      n[        SSS9nU" U5      S	[
        R                  -  [        XP-
  S	-  * S	US	-  -  -  5      -  S	[        [
        R                  -  -  U-  -  :X  d   e[        US	-  S:  5      [        S	[
        R                  -  S	-  5      :X  d   e[        U5      " U5      nU[        [        [        [        S	5      U-  [        S	5      U -  S	U-  -  [!        S	U-  S-
  5      -   -  5      [#        [$        * [$        5      5      [        U 5      5      :X  d   e[        U['        X 5      5      U :X  d   e[)        U5      [        S5      :X  d   eUR*                  R-                  S5      R/                  5       S:X  d   eg )
NmuTrealsigmapositivexr         )r   rm   r	   rA   r@   r   Halfr   r   r>   r)   r   r<   r=   r;   r   r8   r5   oor   rE   rG   compute_expectationdoit)r   r   XYpdfr   anss          \/var/www/auris/envauris/lib/python3.13/site-packages/sympy/stats/tests/test_continuous_rv.pytest_single_normalr   7   s   	4	 B7T*EsAqA	"AQ42::A;%("""
!*CsAFqvvIcAFQ;,%(
344aAFF
l56HIJ K J QTAX;#aik****
1+a.C*\)QtAwrz1U7+VAaC!G_<=+?"b%bM+ + + + Q1	?b   !9	!$$$88''*//1Q666    c                     [        SSS5      n [        X S:  5      n[        S5      n[        U5      " U5      S[        U 5      " U5      -  :X  d   eUR                  R
                  R                  [        S[        5      :X  d   e[        U5      [        S5      [        [        5      -  :X  d   e[        U S-  5      [        US-  5      :X  d   eg )Nr   r   r   zr   )rm   rF   r   r@   rG   domainsetr5   r   r	   r   r   )r   r   r   s      r   test_conditional_1dr   P   s    sAqAaaAsA1:a=A
1----88??(1b/111Q447T"X%%%%QT7a1gr   c                    ^ [        SSS5      m[        TS-  S:*  5      R                  [        SS5      :X  d   e[        TS-  S:*  5      R                  TR                  :X  d   e[        [        TS-  S:*  TS:  5      5      R                  [        SS5      :X  d   e[        [        U4S j5        [        TTS:  5      n U R                  R                  R                  [        S[        5      :X  d   eg )Nr   r   r   r   c                  2   > [        [        T 5      S:  5      $ Nr   )r?   r#   r   s   r   <lambda>'test_ContinuousDomain.<locals>.<lambda>b   s    uSVaZ0r   )rm   r?   r   r5   symbolr3   r   
ValueErrorrF   rG   r   r   )r   r   s    @r   test_ContinuousDomainr   ]   s    sAqAA8B?222A""ahh...QTQYQ'(,,A>>>
:01aaA88??(1b/111r   c                  x   [        SSS5      [        SSS5      p[        SSS9n[        X-   5      S:X  d   e[        X-   5      S:X  d   e[        X -   5      S	:X  d   e[	        X5      S:X  d   e[	        SU -  U-   U * 5      S
[        U 5      -  :X  d   e[        U 5      S:X  d   e[        X-   5      S:X  d   e[        U 5      S:X  d   e[        X-   5      S:X  d   e[        X5      S:X  d   e[        X U-   5      [        X U-
  5      :X  d   e[        U S5      S:X  d   e[        U S5      S:X  d   e[        X-   S	5      S:X  d   e[        U S5      [        U 5      :X  d   e[        X -  S5      S:X  d   e[        X-   S5      [        X-   5      :X  d   e[        X-   S	5      [        X-   5      :X  d   e[        U [        X-   S5      5      S:X  d   e[        U [        X-   S5      5      [        R                  :X  d   e[        U 5      " U5      [        S5      [!        SU-  [        R"                  -
  5      -  :X  d   eg )Nr   r   r   ypTr   r            )rm   r   r	   rA   rB   rC   rD   r   r   r   r   r   r   r   r   r   r8   One)r   r   r   s      r   test_multiple_normalr   i   s/   #q!fS!Q/qsT"AQU8q==AE?aAE?aaq   acAgr"b!n444A;!AE?aA;!AC=Aq!!!qa% Kq5$9999!Q<11a=A!%r!!!1a=HQK'''13?a15!///15!///Q15!"""Ar!%|$...A;q>T!WVAaC!%%K%88888r   c                     [        SSS9u  p[        SSS9u  p#[        SSS9n[        SX5      n[        SX5      n[        S	U5      n[        S
SS9u  pn
[	        U5      U :X  d   e[	        XV-   5      X-   :X  d   e[	        X-  U	-   5      U[	        U5      -  U	-   :X  d   e[        U5      US-  :X  d   e[        XXU-  -   U	-   5      [        U5      US-  [        U5      -  -   :X  d   e[	        U5      SU-  :X  d   e[	        X-  U	-   5      U[	        U5      -  U	-   :X  d   e[	        XXU-  -   U	-   5      XU-  -   U	-   :X  d   e[        U5      [        U 5      :X  d   eg )Nzmu1 mu2Tr   zsigma1 sigma2r   lambdar   r   r   a b cr   r   )r   r   rm   rY   r	   rA   rE   r;   )mu1mu2s1s2rater   r   Zabcs              r   test_symbolicr      sf   yt,HC_t4FB(T*DsCAsCACAgD)GA!Q43;;QU8sy   QS1W:1Q4!###A;"a%A!GaK HQK!Q$x{2B$BBBBQ41T6>>QS1W:1Q4!###Q1Wq[>ST6\A----!9	#&&&r   c                  L  ^^ [        SSS5      m[        T5      n [        TS:  5      U " S5      R                  [        5      :X  d   eU " S5      [
        R                  :X  d   e[        TTS:  5      n U " S5      S:X  d   e[        SS5      m[        T5      n U " S5      S:X  d   e[        TS:  5      SU " S5      -
  :X  d   e[        [        UU4S j5        [        S	S5      n[        U5      nU" [        5      [        S[        [        * 5      -
  [        S:  4S
5      :X  d   eg )Nr   r   r   r   
   r   c                      > [        T T-   5      $ N)rH   r   r   s   r   r   test_cdf.<locals>.<lambda>   s    s1q5zr   r   r   T)rm   rH   r>   rewriter*   r   r   rY   r   r   r   r   r   )dr   fr   r   s      @@r   test_cdfr      s    sAqAAAQU8qt||D))))Q4166>>Aq1uAQ4199CAAAR5A::QU8q1Q4x
:)*CAAAQ49a#qb'k162I>>>>r   c            	         [        SSS5      n [        U 5      nU" S5      [        * S[        [        5      -   -  :X  d   e[	        SSS5      n[        U5      nU" S5      S:X  d   eU" S5      [        [        [
        R                  -
  5      :X  d   e[        SS5      n[        U5      nU" S5      S:X  d   eU" S5      R                  5       [        SS	5      [        S-  S	-  -   :X  d   e[        SSS5      n [        U 5      nU" S5      S:X  d   eU" S5      [        S[        SS
[        -  -
  5      -
  5      :X  d   e[        SSSS5      n [        U 5      nU" S5      S:X  d   eU" S5      S[        -   [        [        SS
5      5      -  S
-  :X  d   e[        SSS5      n[        U5      nU" S5      S:X  d   eU" S5      [        [        S
5      * [        [        * 5      -  5      :X  d   eg )Nr   r   r   r   r   r            r   )ry   rI   r
   r   rm   r   r   rY   expandr   rn   r   rX   rd   )r   cfr   r   Ls        r   test_characteristic_functionr      s   QA	 	#Ba5QBSV$$$$sAqA	 	#Ba5A::a5CAFF
O###CA	 	#Ba5A::a5<<>Xb"-!B6666Q"A	 	#Ba5A::a5CDQqSM)****31a A	 	#Ba5A::a5QUCQ002222S!QA	 	#Ba5A::a5Caqb)****r   c            
         [        SSS9n [        S5      u  pn[        [        SX5      5      " U 5      nU[        U4X-   4U 5      :X  d   e[        [	        SU5      5      " U 5      nU[        S5      U -  [        US-  [        R                  -   5      -  [        US-  [        R                  -   4[        SS5      4U S-  S-  5      -  [        US-  5      -  [        US-  4[        R                  4U S-  S-  5      -   :X  d   e[        [        SU5      5      " U 5      nUSSU -  -
  U* S-  -  :X  d   e[        [        SX5      5      " U 5      nUSX-  -
  U* -  :X  d   e[        [        SXU5      5      " U 5      nU[        X-  US-  U S-  -  S-  -   5      SX-  -
  -  :X  d   e[        [        SU5      5      " U 5      nXAX-
  -  :X  d   e[        [        SX5      5      " U 5      nXB* U -  S-   U* -  :X  d   e[        [!        SX5      5      " U 5      nU[        X -  5      [        U* U -  S-   5      -  :X  d   e[        [#        SX5      5      " U 5      nXB[        U5      -  [%        X-  U5      -  :X  d   e[        ['        SX5      5      " U 5      nU[        X-  5      US-  * U S-  -  S-   -  :X  d   e[        [)        SX5      5      " U 5      nU[        X-  5      [+        U* U -  S-   X -  S-   5      -  :X  d   e[        [-        SX5      5      " U 5      nU[        X-  US-  U S-  -  S-  -   5      :X  d   e[        [/        SX5      5      " U 5      nXBU* U -  U-  -  [1        U* U* U -  5      -  :X  d   e[        [3        SX5      5      " U 5      n[5        U5      S	:X  d   e[        [7        SX5      5      " U 5      nU[8        S-  [        X-  5      -  [;        X -  5      -  X -  US-  U S-  -  [8        S-  -   -  -  :X  d   e[        [=        SU5      5      " U 5      nU[        S5      [        [8        5      -  U-  U -  [?        [        S5      U-  U -  S-  5      S-   -  [        US-  U S-  -  S-  5      -  S-  S-   :X  d   e[        [A        SXU5      5      " U 5      n[5        U5      S
:X  d   e[        [C        SX5      5      " U 5      nU[        X-  5      * [        X -  5      -   X* U-   -  -  :X  d   e[        [E        SU5      5      " U 5      nU[        U 5      S-
  U -  U-  :X  d   e[        [G        SU5      5      " U 5      nUS[I        SX-  5      -  X-  -  :X  d   e[        [        SSS5      5      " U 5      nURK                  U 5      RM                  U S5      [        SSS5      S-  :X  d   e[        [	        SS5      5      " U 5      nURK                  U 5      RM                  U S5      [        S5      [        S[        SS5      4[        R                  5      -  [        [8        5      -  [        [        SS5      4[        SS5      4[        R                  5      -   S[        S5      -  [        S[        SS5      4[        R                  5      -  S[        [8        5      -  -  -   :X  d   e[        [        SS5      5      " U 5      nURK                  U 5      RM                  U S5      [N        :X  d   e[        [        SSS5      5      " U 5      nURK                  U 5      RM                  U S5      S:X  d   e[        [        SSSS5      5      " U 5      nURK                  U 5      RM                  U S5      [        S5      * :X  d   e[        [        SS5      5      " U 5      nURK                  U 5      RM                  U S5      S:X  d   e[        [        SSS5      5      " U 5      nURK                  U 5      RM                  U S5      S:X  d   e[        [!        SSS5      5      " U 5      nURK                  U 5      RM                  U S5      [P        S-   :X  d   e[        [#        SSS5      5      " U 5      nURK                  U 5      RM                  U S5      [R        * [U        SSS5      -  :X  d   e[        ['        SSS5      5      " U 5      nURK                  U 5      RM                  U S5      S:X  d   e[        [)        SSS5      5      " U 5      nURK                  U 5      RM                  U S5      [+        SS5      :X  d   e[        [-        SSS5      5      " U 5      nURK                  U 5      RM                  U S5      [        [        R                  5      :X  d   e[        [/        SSS5      5      " U 5      nURK                  U 5      RM                  U S5      [%        SS5      :X  d   e[        [3        SSS5      5      " U 5      nURK                  U 5      RM                  U S5      S[R        -  S[        S5      -  -
  :X  d   e[        [7        SSS5      5      " U 5      nURK                  U 5      RM                  U S5      S[R        -  [8        S-  -  [;        S5      -  S[8        S-  -   S-  -  [R        [8        S-  -  [W        S5      -  S[8        S-  -   -  -   :X  d   e[        [=        SS5      5      " U 5      nURK                  U 5      RM                  U S5      [        S5      [        [8        5      -  S-  :X  d   e[        [A        SSSS5      5      " U 5      nURK                  U 5      RM                  U S5      [R        * [        S5      -   :X  d   e[        [C        SSS5      5      " U 5      nURK                  U 5      RM                  U S5      S:X  d   e[        [E        SS5      5      " U 5      nURK                  U 5      RM                  U S5      S:X  d   e[        [G        SS5      5      " U 5      nURK                  U 5      RM                  U S5      S[I        SS5      -  [I        SS5      -   [I        SS5      -   :X  d   eg )NtTr   r   r   r   r   r   zk(3*(t*(-4*b + (a + b)**2) + 4)*exp(b*t) - 3*(t*(a**2 + 2*a*(b - 2) + b**2) + 4)*exp(a*t))/(t**2*(a - b)**3)zb(-2*(-a + b)*exp(c*t) + 2*(-a + c)*exp(b*t) + 2*(b - c)*exp(a*t))/(t**2*(-a + b)*(-a + c)*(b - c)))r   )r   )r   r   r   ) )r   r   ))r   r   r   r   ir   ),r   rJ   rN   r1   rR   r   r-   r   r   r   rS   rW   rX   r   rY   r^   ra   r`   r,   rc   re   r(   rm   ro   r/   rq   strrr   r   r   rs   r)   rx   ry   rz   r~   r%   r   subsr
   r   er:   r   )r   r   r   r   mgfs        r   test_moment_generating_functionr      s   d#A gGA!
$T#q_
5a
8C%quh****
$Sa[
1!
4C$q'!)E!A#,//qsQVV|oA0!Q$q&9::?!*EqsfqvviAa() ) ) ) %ZQ%7
8
;C1qs7qbd####
$VC%6
7
:C1qs7qb/!!!
$ZQ1%=
>q
AC#acAqDAIaK'(!ac'2222
$[a%8
9!
<CQU)
$U3%5
6q
9C2a4!8r""""
$VC%6
7
:C#ac(5!A?****
$Xc1%8
9!
<CCF(6!#q>))))
$WS!%7
8
;C#ac(QTE!Q$JN++++
$Xc1%8
9!
<C#ac(41q!#'22222
$VC%6
7
:C#acAqDAIaK'((((
$VC%6
7
:CaRTAI+j!aRT22222
$ZQ%:
;A
>Cs8 H I I I %\#q%<
=a
@C"a%AC.ac*ACAadRU1B,CDDDD
$Xc1%5
6q
9C$q'$r("1$Q&DGAIaKM(:Q(>?	QT!Q$Yq[	        %ZQ1%=
>q
ACs8 ; < < < %WS!%7
8
;CCH9s13x'!R!V*5555
$ZQ%7
8
;CCFQJ>A%%%%
$%5c1%=
>q
AC!GAqsO#QS)))) %T#q!_
5a
8C88A;Aq!U4q%9!%;;;;
$Sa[
1!
4C88A;Aq!T!WU4(1a.9JAFF . &
2h&A(8Aq>*;QVVD&EGHayQVW[a^qvvR H !$r(
H,&, , , , %ZQ%7
8
;C88A;Aq!Q&&&
$VCA%6
7
:C88A;Aq!Q&&&
$ZQ1%=
>q
AC88A;Aq!c!fW,,,
$[a%8
9!
<C88A;Aq!Q&&&
$U31%5
6q
9C88A;Aq!Q&&&
$VCA%6
7
:C88A;Aq!Z!^333
$Xc1a%8
9!
<C88A;Aq!aRQ) &    %WS!Q%7
8
;C88A;Aq!Q&&&
$Xc1a%8
9!
<C88A;Aq!T!QZ///
$VCA%6
7
:C88A;Aq!S[000
$VCA%6
7
:C88A;Aq!VAq\111
$ZQ%:
;A
>C88A;Aq!SUQs1vX%5555
$\#q!%<
=a
@C88A;Aq!RT"a%ZQ%7QYN&r1uWT!W_a"a%i0&1 1 1 1 %Xc1%5
6q
9C88A;Aq!T!WT"X%5a%7777
$ZQ1%=
>q
AC88A;Aq!aR#a&[000
$WS!Q%7
8
;C88A;Aq!Q&&&
$ZQ%7
8
;C88A;Aq!Q&&&
$%5c1%=
>q
AC88A;Aq!R1%51%E1&   r   c                     [        S5      [        [        S-  * S-  5      -  S[        [        5      -  -  n [	        [        U SS9n[        SSS5      n[        U5      [        U5      :X  d   e[        US:  5      [        US:  5      :X  d   e[	        [        [        [        * 5      [        S[        5      S9nUR                  R                  R                  [        S[        5      :X  d   e[        U5      S:X  d   e[        US:  5      [        S	5      :X  d   e[        [         S
 5        [#        SSS9u  pEnS[%        U5      Xe-  -  -  XES-
  -  -  [        U* U-  5      -  n [	        X@[        S[        5      S9n['        SXV5      n[        U5      [        U5      -
  R)                  5       S:X  d   e[        U5      [        U5      -
  R)                  5       S:X  d   eg )Nr   T)checkr   r   r   r   r   r   c                  R    [        [        [        [        * 5      [        SS5      SS9$ )Nr   r   T)r   r   )rK   r   r   r5   r   r   r   r   #test_ContinuousRV.<locals>.<lambda>f  s    |AsA2wHQOSWXr   z	x k thetar   )r   r   r   r   rK   rm   rA   r>   r   r5   r   rG   r   r   r	   r   r   r   r-   r^   r6   )r   r   r   r   _xkthetas          r   test_ContinuousRVr   Z  s   
q'#q!teAg,
$r(

+CQ4(AsAqAA;(1+%%%QU8qQxQQBXa_5A88??(1b/111Q4199QU8s2w
:XY ;6LB5
U1Xeh
qS	
)#rc%i.
8CR(1b/2Ac1AaD1Q4K!!#q(((QK(1+%//1Q666r   c                     [        SSS9n [        SSS9n[        SX5      n[        U5      " [        5      S[        [        [        * U-   [        U -
  -  5      -  -  :X  d   e[        U5      " [        5      [        SU [        :  4S[        [        U * [        -   U * U-   -  5      5      -  [        -  U[        :  4S	5      :X  d   e[        U5      R                  R                  [        X5      :X  d   eg )
Nr   Tr   r   r   r   r   r   r   T)r   rL   r@   r   r   r   rH   r   r    rG   r   r   r5   r   r   r   s      r   test_arcsinr   r  s    sAsAsAA1:a=Ar$QQ'7"889999q6!9	1a!e*tD1"q&A26):$;<<R?aH%' ' ' ' !98A>111r   c            
        ^ ^^^ [        SSS9m[        SSS9m[        SSS9m[        STTT5      m [        T 5      " [        5      T[        -  ST-  [	        [        T-  5      -  [        -  -   [        T* [	        [        T-  5      -  T[	        [        T-  5      S-  -  -
  5      -  :X  d   e[        T 5      R                  R                  [        T[        5      :X  d   e[        [        U 4S j5        [        SSS	9m[        [        UUU4S
 j5        [        SSS	9m[        [        UUU4S j5        [        SSS9m[        [        UUU4S j5        [        SSS9m[        SSS	9m[        [        UUU4S j5        g )NalphaTr   r(   r   r   r   c                     > [        T 5      $ r   rJ   r   s   r   r   test_benini.<locals>.<lambda>      (B1(Er   nonpositivec                      > [        ST TT5      $ Nr   rM   r   r(   r   s   r   r   r         vc5$>r   c                      > [        ST TT5      $ r  r  r  s   r   r   r     r  r   c                      > [        ST TT5      $ r  r  r  s   r   r   r     r  r   c                      > [        ST TT5      $ r  r  r  s   r   r   r     r  r   )r   rM   r@   r   r   r   rG   r   r   r5   r   r   NotImplementedErrorr   )r   r   r(   r   s   @@@@r   test_beninir
  ~  sC   7T*E&4(D7T*EsE4'A1:a=eAg$s1U7|(;A(==vc!E'l2T#ag,/5IIJK L L L !98E2#6666
 EF7-E
:>?&d+D
:>?7T*E
:>?&4(D7-E
:>?r   c                     [        SSS9u  p[        SX5      n[        U5      R                  R                  [        SS5      :X  d   e[        U5      " [        5      [        U 4X-   4[        [        -  5      :X  d   e[        U5      " [        5      [        U S-
  -  S[        -
  US-
  -  -  [        X5      -  :X  d   e[        [        U5      5      X U-   -  :X  d   e[        [        U5      5      X-  U S-  SU S-  -  U-  -   U S-  -   SU -  US-  -  -   SU -  U-  -   US-  -   US-  -   -  :X  d   eS	u  p[        SX5      n[        [        U5      5      U [!        X-   5      -  :X  d   e[        [        U5      5      X-  [!        X-   S-  X-   S-   -  5      -  :X  d   e[#        U5      [%        SS['        S5      -  -
  5      :X  d   eg )
Nz
alpha betaTr   r   r   r   r   r   )r   r   )r   rN   rG   r   r   r5   rI   r   r1   r
   r@   r(   r6   r	   rA   r   r   rE   r;   r   )r   r   Bs      r   	test_betar    s   <$/DAS!A!98Aq>111"1%a(E1$!A#,FFFF1:a=AAJAQ'77Q
BBBBAaD>Qa%[(((HQK AC1a4!AqD&(?QT+AAaC1H+LqQRsSTu+TWXZ[W[+[^_ab^b+b$cccc DAS!AqtAaeH,,,x{#q!%!quqy1I/J'JJJJ!9	!aQi-0000r   c                  2  ^^^ [        SSS9u  mm[        SSS9m[        S5      n [        STTT5      n[	        U5      R
                  R                  [        SS	5      :X  d   e[        U5      n[        S
5      n[        X0T-   S	-
  -  TS-  U -  -  S	U-
  TS	-
  -  -  [        T* S-  5      -  [        U T-   T5      [        U 5      -  -  U S[        45      nU" U5      R                  U5      (       d   e[        S5      u  mmm[        STTT5      (       d   e[        SSSS9m[        [         UUU4S j5        [        SSS9m[        SSSS9m[        [         UUU4S j5        [        SSS9m[        SSS9m[        SSSS9m[        [         UUU4S j5        g )Na bTr   r   )nonnegativer   r   r   r   r   r   r   r   Fr   r   c                      > [        ST TT5      $ r  rO   r   r   r   s   r   r   &test_beta_noncentral.<locals>.<lambda>      ~c1a;r   r   c                      > [        ST TT5      $ r  r  r  s   r   r   r    r  r   )r  r   c                      > [        ST TT5      $ r  r  r  s   r   r   r    r  r   )r   r   r   rO   rG   r   r   r5   r@   r   r   r(   r   r   dummy_eqr   r   )_kr   densr   resr   r   r   s        @@@r   test_beta_noncentralr    s   54(DAqs%A	sBsAq!$A!98Aq>1111:DsA
q6A:!by(!a%1q5)99#qbd)CR!VQ	"-/13Q=C7C     gGAq!#q!Q''''sU.A
:;<sT"AsU.A
:;<sT"AsT"AsD1A
:;<r   c                    ^^ [        SSS9m[        SSS9m[        STT5      n [        U 5      " [        5      [        TS-
  -  [        S-   T* T-
  -  -  [	        TT5      -  :X  d   e[        SSS9m[        [        UU4S j5        [        SSS9m[        SSS9m[        [        UU4S	 j5        [        SSS5      n [        U 5      [        S5      :X  d   eg )
Nr   Tr   r(   r   r   r   c                     > [        ST T5      $ r  rP   r   betaps   r   r    test_betaprime.<locals>.<lambda>      yeU;r   c                     > [        ST T5      $ r  r   r!  s   r   r   r#    r$  r   )	r   rP   r@   r   r(   r   r   rE   r;   )r   r   r"  s    @@r   test_betaprimer&    s    7T*E6D)E#ue$A1:a=A	NAEeVe^+DDT%QVEWWWWW7-E
:;<7T*E6t,E
:;<#q!A!9	!$$$r   c                    ^^ [        SSS9u  mm[        [        UU4S j5        [        SSS9u  mm[        [        UU4S j5        [        SSS9u  mm[        [        UU4S	 j5        [        S
STT5      n U R                  R
                  R                  [        TT5      :X  d   e[        U 5      " [        5      STS-  -  [        S-  STS-  TS-  -  -
  -  -  :X  d   e[        U 5      " [        5      [        TS-  * TS-  -  [        S-  TS-  TS-  -
  -  -  TS-  TS-  TS-  -
  -  -   T[        :*  4S5      :X  d   e[        U 5      R                  5       ST-  T-  TT-   -  :X  d   e[        S
SSS5      n [        U 5      R                  5       [        S5      :X  d   e[        U 5      [!        [#        SS5      5      :X  d   e[%        U 5      R                  5       SS[        S5      S-  -  -
  :X  d   eg )NzL, HTnegativec                      > [        SSTT 5      $ Nr   r   r   Hr   s   r   r   $test_BoundedPareto.<locals>.<lambda>      }S!Q:r   Fr   c                      > [        SSTT 5      $ r+  r,  r-  s   r   r   r/    r0  r   r   c                      > [        SSTT 5      $ )Nr   r   r,  r-  s   r   r   r/    s    }S"a;r   r   r   r   r   r   r         )r   r   r   r   rG   r   r   r5   r@   r   rH   r   r	   r6   r   rE   r;   r   rA   )r   r.  r   s    @@r   test_BoundedParetor5    s   6D)DAq
::;6&DAq
::;6D)DAq
:;<c1a#A88??(1a.0001:a=AadFAqD!ad1a4i-$89999q6!9	AqD5A:q!tQTAqD[/A#BdAqD1a4K0$123q&#:;DF F F FQ4==?ac!eQUm+++c1a#AQ4==?c"g%%%!9	(1a.1111A;!QCFAI%5555r   c                  0  ^^^^ [        SSS9m[        SSS9m[        SSS9n [        STT5      m[        T5      " [        5      [	        T* [        [        5      -  [        [        -  T-  -   5      :X  d   e[        [        U4S j5        [        T5      " [        5      S	[        T-  S	[        T-
  S
-  TS
-  -  -   -  -  :X  d   e[        [        T5      " [        5      [        5      [        T5      " [        5      :X  d   e[        T5      " U 5      T[        [        U [        R                   -
  -  5      -  T-   :X  d   e[        SSS9m[        ["        UU4S j5        [        SSS9m[        ["        UU4S j5        [%        T5      ['        T5      :X  d   eg )Nx0Tr   r-   r   r   r   c                     > [        T 5      $ r   r   r   s   r   r   test_cauchy.<locals>.<lambda>  r   r   r   r   x1Fc                     > [        STT 5      $ r  rQ   )r-   r:  s   r   r   r9        vc2u5r   r   c                     > [        STT 5      $ r  r<  )r-   r7  s   r   r   r9    r=  r   )r   rQ   rI   r   r   r   r
   r   r	  r@   r   r   rH   r   r$   r   r   r   rE   r;   )r   r   r-   r7  r:  s    @@@@r   test_cauchyr?    sI   	4	 B7T*EsT"AsBA"1%a(Cs1v!B0F,GGGG
 EF1:a=Ar%xa"fq[-A)ABCCCCAq	1A...A;q>U3r1qvv:#77"<<<<	5	!B
:567-E
:56!9	"%%%r   c                  X  ^ SSK Jn   [        SSS9m[        ST5      n[	        U5      " [
        5      ST* S-  S-   -  [
        TS-
  -  -  [        [
        S-  * S-  5      -  [        TS-  5      -  :X  d   e[        U5      " [
        5      [        S5      U -  [
        -  [        TS-  [        S5      S-  -   5      -  [        TS-  [        S5      S-  -   4[        S	5      S-  4[
        S-  * S-  5      -  [        TS-  5      -  [        TS-  4[        S5      S-  4[
        S-  * S-  5      -   :X  d   e[        U5      " [
        5      [        S5      [
        -  [        TS-  [        S5      S-  -   5      -  [        TS-  [        S5      S-  -   4[        S	5      S-  4[
        S-  S-  5      -  [        TS-  5      -  [        TS-  4[        S5      S-  4[
        S-  S-  5      -   :X  d   e[        SSS
S9m[        [        U4S j5        [        SS
SS9m[        [        U4S j5        g )Nr   )r
   r   Tintegerr   r   r   r   FrB  r   c                     > [        ST 5      $ r  rR   r   s   r   r   test_chi.<locals>.<lambda>      s3{r   c                     > [        ST 5      $ r  rE  rF  s   r   r   rG    rH  r   )sympy.core.numbersr
   r   rR   r@   r   r   r-   rI   r   r   r1   rJ   r   r   )r
   r   r   s     @r   test_chirK    sQ   $sD!ACA1:a=A1qM!a!e*4S!Q$q\A%!*LLLL #1%a(DGAIaKacAaDFl8K,KESTUVSVYZ[\Y]^_Y_S_Ra-.qT!VI1uQwM@ -@@Eac
-KMRTUVWTWSY\]^_\`ab\b[dghjkgkfklmfmMn-o o o o &a(+tAwqyqsQqT!V|9L/LUTUVWTWZ[\]Z^_`Z`T`Sb121a	1a46NC 0CCH1:0NPUWXYZWZV\_`ab_cde_e^gijlmimnoioPp0q q q q 	sD51A
:*+sED1A
:*+r   c                    ^^ [        SSS9m[        S5      m[        STT5      n [        U 5      " [        5      [        T-  T-  [        T-  T* S-  -  -  [	        [        S-  * S-  TS-  S-  -
  5      -  [        TS-  S-
  [        T-  5      -  :X  d   e[        SSSS	9m[        [        UU4S
 j5        [        SSSS	9m[        SSS9m[        [        UU4S j5        [        SSS9m[        SSS9m[        [        UU4S j5        g )Nr   TrA  lr   r   r   FrC  c                     > [        ST T5      $ r  rT   r   rM  s   r   r   %test_chi_noncentral.<locals>.<lambda>       }S!Q7r   r   c                     > [        ST T5      $ r  rO  rP  s   r   r   rQ  $  rR  r   r   c                     > [        ST T5      $ r  rO  rP  s   r   r   rQ  (  rR  r   )r   rT   r@   r   r   r%   r   r   )r   r   rM  s    @@r   test_chi_noncentralrU    s   sD!AsAc1a A1:a=QT!VQqSQBqDM1q!teAg1Q./007!a10EF G G G 	sD51A
:78sD40As%A
:78sE"AsT"A
:78r   c                    ^ [        SSS9m[        ST5      n [        U 5      " [        5      S[        -  [        -  S-   T* S-  -  :X  d   e[        U 5      " [        5      ST* S-  -  [        TS-  S-
  -  -  [        [        * S-  5      -  [        TS-  5      -  :X  d   e[        U 5      " [        5      [        [        TS-  [        S-  5      [        TS-  5      -  [        S:  4S	5      :X  d   e[        U 5      T:X  d   e[        U 5      ST-  :X  d   e[        SS
5      n [        U 5      " S5      S[        S5      -  [        [        SS5      5      -  S[        [        5      -  -  [!        [        S5      S-  5      -   :X  d   e[        SSSS9m[#        [$        U4S j5        [        SSSS9m[#        [$        U4S j5        g )Nr   TrA  r   r   r   r   r   r      r   i   i  FrC  c                     > [        ST 5      $ r  rS   rF  s   r   r   "test_chi_squared.<locals>.<lambda>;      z#q1r   c                     > [        ST 5      $ r  r[  rF  s   r   r   r\  >  r]  r   )r   rS   rI   r   r
   r@   r   r-   rH   r   r.   r	   rA   r   r   r   r)   r   r   )r   r   s    @r   test_chi_squaredr_  +  s   sD!A3A #1%a(bd1fqjQBqD-ABBB1:a=A1Ia!A#'l23r!t9<U1Q3ZGGGGq6!9	:ac1Q3#7ac
#BAF"KYWWWWQ4199A;!A#3Aq6!9tAws8B?';;T$r(]KcRVWXRYZ[R[n\\\\sD51A
:12sED1A
:12r   c                    ^^^ [        SSS9m[        SSS9m[        SSS9m[        STTT5      n [        U 5      " [        5      TT-  [        T-  TT-  -  -  [        T-  T-  S-   T* S-
  -  -  [        -  :X  d   e[	        U 5      " [        5      [        S[        T-  T* -  -   T* -  [        S:  4S	5      :X  d   e[        SSS
9m[        [        UUU4S j5        [        SSS9m[        SSS
9m[        [        UUU4S j5        [        SSS9m[        SSS
9m[        [        UUU4S j5        [        SSSS5      n [        U 5      [        S5      :X  d   eg )Nr   Tr   r   r   r   r   r   r   r   c                      > [        STT T5      $ r  rU   r   r   r   s   r   r   test_dagum.<locals>.<lambda>L      uS!Q2r   c                      > [        STT T5      $ r  rb  rc  s   r   r   rd  P  re  r   c                      > [        STT T5      $ r  rb  rc  s   r   r   rd  T  re  r   )
r   rU   r@   r   rH   r   r   r   rE   r;   )r   r   r   r   s    @@@r   
test_dagumrh  A  sL   sT"AsT"AsT"Ac1aA1:a=AaC1!,qsQhlqb1f-EEaGGGGq6!9	A1Or#:AF"C$-/ / / / 	s%A
:23sT"As%A
:23sT"As%A
:23c1aA!9	!$$$r   c                     [        SSS9n [        SSS9n[        SSS9n[        SXU5      nX-  [        U-
  SU-
  -  -  n[        U [        U-
  -  5      S-
  [	        U5      [        U5      -  -  n[        U5      " [        5      XE-  :X  d   eg )	Nr   Tr   nr   r   r   r   )r   rV   r   r   r-   r0   r@   )r   rj  r   r   dividenddivisors         r   
test_davisrm  X  s    sT"AsT"A	t	$Bc1AtQVr!t$$H1ad8}Qq$q'!12G1:a=H,,,,r   c                  n   [        SSSS9n [        SSS9n[        SX5      n[        U5      " [        5      [        U S-
  -  X-  -  [	        [        * U-  5      -  [        U 5      -  :X  d   e[        U5      " [        5      [        [        X[        -  5      [        U 5      -  [        S:  4S	5      :X  d   eg )
Nr   TrC  rM  r   r   r   r   r   )	r   rW   r@   r   r   r-   rH   r   r.   )r   rM  r   s      r   test_erlangro  c  s    sD40AsT"AsAA1:a=AAJqtOC1I5eAh>>>>q6!9	:a1#5eAh#>A"F(* * * *r   c            	         [        S5      u  p[        SSS9u  p#[        SXU5      n[        U5      " U5      U[        X3US-  -  SU -  -   SU-  -
  -  S-  5      -  [	        [        S5      X2S-  -  U -   U-
  -  SU-  -  5      -  S-  :X  d   eX1U -
  -  nX2-  n[        [        SSU5      5      " U5      n[        [        SUS-  U5      5      " U5      nU[        U* US-  S-  -   [        U5      -   5      -
  n	[        U5      " U5      U	:X  d   e[        U5      R                  5       US-  US-  -   :X  d   e[        U5      R                  5       SUS	-  US-  -  [        US-  US-  -   5      -  U[        US-  US-  -   5      -  -   -  :X  d   eg )
Nzm, zzs, lTr   r   r   r   r   r   )r   rX   r@   r   r*   r   rH   rm   r   rA   r   rC   )
mr   srM  r   uvGaussianCDF1GaussianCDF2actual_outputs
             r   test_exgaussianrx  m  s   6?DA6D)DA3a A1:a=Ac!q!tVac\AaC%7"8":;;T!Wa1fqj1n%qs+,--./ / / / 	
q5	A	Avc1a()!,Lvc1a4+,Q/L 3rQT!V}s<7H'H#IIMq6!9%%% A;1a4!b'>111A;1ad1a4iQTAG^0D&Dq&*1a4!b'>&:H; '; $< < < <r   c            
      t   [        SSS9n [        SU 5      n[        SSSS9n[        U5      SU -  :X  d   e[        U5      SU S-  -  :X  d   e[	        U5      S:X  d   e[	        U5      [        US	5      :X  d   e[        U5      S
:X  d   e[        U5      [        US5      :X  d   e[        SU-  S5      [        US5      :X  d   e[        US	5      SU S	-  -  :X  d   e[        US:  5      [        R                  L d   e[        US:  5      [        U * 5      :X  d   e[        US:  5      [        SU -  5      :X  d   e[        U5      " U5      [        SU-
  5      * U -  :X  d   e[        US:*  5      R                  [!        SS5      :X  d   e[        SS5      n[#        U5      [%        [        S5      5      :X  d   e['        S5      n[        X:  5      [        U* U -  5      :X  d   e[        X:  5      S:X  d   e[        S5      n['        S5      n[)        U[+        S5      5      n[-        [.        5         [1        S[        SU-  5      -  US	[2        45      nUR5                  US	:  SS9R7                  [0        5      R9                  U5      (       d   e[1        S[        SU-  5      -  USS45      n	UR5                  US:  SS9R7                  [0        5      R9                  U	5      (       d   e S S S 5        [        SSU -  5      n[;        XU5      [	        U5      :X  d   e[;        XX-  -   USU -  U-  -   5      S[=        SSSU S-  -  -  -   5      [=        SSSU S-  -  -  -   5      -  -  :X  d   e[;        USU-  -   X1-   USU-  -   US	:  5      [=        S5      [?        S
S5      -  :X  d   eg ! , (       d  f       N= f)Nr   Tr   r   r   r  r   r   r   	   r   rX  r   r   ir   r   _zr   Fevaluate   U   ) r   rY   r	   rA   rC   r   rD   r   r>   r   r   r   r   r   r?   r   r5   rE   r;   r   r   r   r   UserWarningr2   r   probabilityr   r  r}   r   r   )
r   r   r   r   r   r   r{  r   	expected1	expected2s
             r   test_exponentialr    s   (T*DCAsT-AQ41T6>>A;!D!G)###A;!A;'!Q-'''A;!A;'!Q-'''1Q3?gam+++!Q<5q=(((QU8quuQU8sD5z!!!QV9CH%%%A;q>c!A#hYt^+++a=A...CA!9	#a&))))c
AQU8sA2d7|###QU8q==sA	tBq"9!"<=A		%Qs2b5z\B2;7	}}QUU}3;;HENNyYYYYQs2b5z\B1:6	}}QUU}3;;HENNyYYYY 
& 	C4 AaA(1+---aTVQ4\24AqqyM 124AqqyM8I3JJKL L La!A#gqua!A#gq1u5S	(1b/12 2 2 
&	%s   1B9N))
N7c            	         [        S5      n [        S5      n[        SSS9n[        SSS9n[        SXU5      n[        U5      " U5      U[        [	        X-
  5      U-  U-  * 5      -  SU-  [        S	U-  5      -  -  :X  d   e[        U5      " U5      [        R                  [        S	U-  [	        X-
  5      U-  U-  5      [        U * U-   5      -  S[        S	U-  5      -  -  -   :X  d   eg )
Nr   r   r   Tr   r(   r   r   r   )r   rZ   r@   r   r   r-   rH   r   r   r.   r   )r   r   r   r(   r   s        r   test_exponential_powerr    s   	BsA7T*E&4(Db.A1:a=Ds26{5'8(,'- &- ". ./0wuQtV}/DF F F Fq6!9AdF [.5"77;RC!G}"E!"54="2 2 2 2 2r   c                  J  ^ ^^ [        SSS9m[        SSS9m[        STT5      m [        T 5      " [        5      TTS-  -  [	        T[        -  T-  T[        -  T-   T* T-
  -  -  5      -  [        [        TS-  TS-  5      -  -  :X  d   e[        [        U 4S j5        [        SSS9m[        [        U4S	 j5        [        SSS
S9m[        [        U4S j5        [        SSS9m[        SSS9m[        [        UU4S j5        [        SSS
S9m[        [        UU4S j5        g )Nd1Tr   d2r   r   c                     > [        T 5      $ r   r   r   s   r   r   %test_f_distribution.<locals>.<lambda>  r   r   r   c                     > [        ST T 5      $ r  r[   r  s   r   r   r        }S"b9r   F)r   rB  c                     > [        ST T 5      $ r  r  r  s   r   r   r    r  r   c                     > [        ST T5      $ r  r  r  r  s   r   r   r    r  r   c                     > [        ST T5      $ r  r  r  s   r   r   r    r  r   )	r   r[   r@   r   r   r(   r   r	  r   )r   r  r  s   @@@r   test_f_distributionr    s   	t	$B	t	$Bc2r"A1:a=R"Q$ZbdRZArcBh8O-O(PP bdBqD!113 4 4 4  EF	$	'B
:9:	tU	3B
:9:	t	$B	$	'B
:9:	tU	3B
:9:r   c                  2   [        SSS9n [        SSS9n[        SX5      n[        U5      " [        5      SX S-  -  -  XS-  -  -  U [	        S[        -  5      -  U-   U * S-  US-  -
  -  -  [	        U [        -  5      -  [        U S-  US-  5      -  :X  d   eg )Nr  Tr   r  r   r   )r   r\   r@   r   r   r(   )r  r  r   s      r   test_fisher_zr    s    	t	$B	t	$BRA1:a=QrqDz\"!t*4bQqSkB6F!#A16. ..1"Q$i88<RT2a48HI J J Jr   c                  ~   [        SSS9n [        SSS9n[        SSS9n[        SXUS9n[        U5      " [        5      U [        U-
  U-  U * S	-
  -  -  [	        [        U-
  U-  U * -  * 5      -  U-  :X  d   e[        U5      " [        5      [        [	        U* [        -   U-  U * -  * 5      U[        :*  4S
5      :X  d   eg )Nr   Tr   rr  rq  r   r   )rr  rq  r   r   )r   r]   r@   r   r   rH   r   )r   rr  rq  r   s       r   test_frechetr    s    sT"AsT"AsAQq!A1:a=AAqyQBF33C1q5!)r9J8J4KKAMMMMq6!9	31"q&!r(:':#;Q!V"DiPPPPr   c            
         [        SSS9n [        SSS9n[        SX5      n[        U5      " [        5      [        * U-  [        -  S-   U * -  :X  d   e[        U5      " [        5      [        U S-
  -  X* -  -  [        [        * U-  5      -  [        U 5      -  :X  d   e[        USS9" [        5      [        U * [        U S5      -  [        U S-   5      -  U [        U [        U-  5      -  [        U S-   5      -  -   [        S:  4S	5      :X  d   e[        U5      [        US5      :X  d   e[        S
SS9u  p[        SX5      n[        U5      X-  :X  d   e[        U5      XS-  -  :X  d   e[!        U5      R#                  5       S[%        U 5      -  :X  d   e['        U5      R#                  5       SSU -  -   :X  d   e[        SSU -  SU-  5      n[)        X!U-  U-   X-  U-   5      R+                  5       SSU * -  -  [%        U 5      -  U-  SSSU -  -  -  SSU -  -  -
  -  [%        U S-  S-   5      [%        US-  S-   5      -  -  :X  d   eg )Nr   Tr   r   r   r   r9   r   r   zk thetar   r   rX  r   i r      )r   r^   rI   r   r
   r@   r   r-   rH   r   r   r.   r	   r   r   rA   rC   r   r   rD   r}   r6   )r   r   r   r   s       r   
test_gammar    sT   sT"A7T*Ec1A #1%a(qbhqj1n-CDDD1:a=AAJur{23r%x=@qIIIIq$"iR
1a  q1u-*Q%((q1u5678Av?'    Q46!Q<y40HAc1AQ417??A;!1H*$$$A;1T!W9,,,A;1qs7***c1Q3% Aaq1acAg.779	&A2,tAwu$aBqD	kAfaiK&?@
q!tby/$uax"}-
-	// / /r   c            
      x  ^ [        SSS9n [        SSS9n[        SX5      m[        T5      " [        5      [        U * S-
  -  X-  -  [	        U* [        -  5      -  [        U 5      -  :X  d   e[        T5      " [        5      [        [        X[        -  5      [        U 5      -  [        S:  4S5      :X  d   e[        T5      " [        5      S	[        * U-  [        -  U S	-  -  -  [        U S	[        U5      -  [        [        * [        -  5      -  5      -  [        U 5      -  :X  d   e[        [        U4S
 j5        g )Nr   Tr   r   r   r   r   r   r   c                     > [        T 5      $ r   r   r   s   r   r   $test_gamma_inverse.<locals>.<lambda>  r   r   )r   r_   r@   r   r   r-   rH   r   r/   rI   r
   r'   r   r   r	  r   s     @r   test_gamma_inverser  	  s   sT"AsT"AS!A1:a=AQK,S!AY6uQx????q6!9	:a1#5eAh#>A"F	RRRR"1%a(A!Aa1Q3,?a4741:-.-//4Qx-8 8 8 8
 EFr   c            
         [        SSS9n [        SSS9n[        SX5      n[        U5      " [        5      X-  [	        U5      -  [	        U [        -  5      -  [	        U* [	        U [        -  5      -  5      -  :X  d   e[        U5      " [        5      S[	        U5      [	        U* [	        U [        -  5      -  5      -  -
  :X  d   e[        [        U5      " [        5      [        5      [        U5      " [        5      :X  d   eg Nr   Tr   etar   r   )r   r`   r@   r   r   rH   r   r   r  r   s      r   test_gompertzr    s    sT"A

&CaA1:a=AE#c(N3qs83CS1X4FFFFFq6!9CHS#c!A#h%777777Aq	1A...r   c            	      P   [        SSS9n [        S5      n[        S5      n[        S5      n[        SX5      n[        SXSS9n[        U5      " U5      R                  5       [	        X-  5      [	        U* U -  5      -  [	        [	        X-  5      * [	        U* U -  5      -  5      -  U -  :X  d   e[        U5      " U5      R                  5       [	        U* U -  5      [	        X0-  5      -  [	        [	        U* U -  5      * [	        X0-  5      -  5      -  U -  :X  d   e[        U5      " U5      R                  5       [	        [	        X-  5      * [	        U* U -  5      -  5      :X  d   e[        U5      " U5      [	        [        U-  U-  5      [        [        * U -  U-  S-   5      -  :X  d   eg )	Nr(   Tr   r   r   r   )minimumr   )	r   ra   r@   r   r   rH   rI   r
   r-   )r(   r   r   r   r   r   s         r   test_gumbelr    s   &4(D	BsAsAsDAsDd+A1:a=!LaRWc3rw<-QBtG"<==dBC C C1:a=!DM#af+c3s4x=.QV"<==dBC C Cq6!9RWc1"T'l"#$ $ $"1%a(C"QKqbgai!m8L,LLLLr   c                  V   [        SSS9n [        SSS9n[        SX5      n[        U5      " [        5      [        U S-
  -  U -  U-  [        U -  * S-   US-
  -  -  :X  d   e[	        U5      " [        5      [        S[        S:  4[        U -  * S-   U-  * S-   [        S:*  4S5      :X  d   eg )	Nr   Tr   r   r   r   r   r   )r   rb   r@   r   rH   r   r   s      r   test_kumaraswamyr  -  s    sT"AsT"ACA1:a=AAJqLNQTEAIQ+?????q6!9	1a!e*$%qD519q.1!4a1f = )+ + + +r   c                     [        S5      n [        SSS9n[        SX5      n[        U5      " [        5      [	        [
        U -  [        -  5      US-  [        S-  -  S-   -  :X  d   e[        U5      " [        5      [	        [        [        U -
  5      * U-  5      SU-  -  :X  d   e[        U5      " [        5      [        [	        U * [        -   U-  5      S-  U [        :  4[	        U [        -
  U-  5      * S-  S-   S45      :X  d   e[        SSS/SS/SS//5      n[        [        U5      R                  [        5      (       d   eg )	Nr   r   Tr   r   r   r   r   )r   rc   rI   r   r   r
   r@   r   rH   r   
isinstancerG   distributionr   )r   r   r   s      r   test_laplacer  8  s.   	BsT"ARA #1%a(S2a[!Q$q!t)a--HIII1:a=CQVQ/15555q6!9	3a{#3A#5rAv">!261*o-a/!3T:< < < <aVq!fq!f-.AfQi,,.MNNNNr   c            	        ^ ^^ [        SSS9m[        SSS9m[        STT5      m T R                  R                  R                  [        T[        5      :X  d   e[        T 5      " [        5      [        TS[        -  -  5      [        T* S[        T-
  -  -  5      -  [        T-
  [        R                  [        R                  -   -  -  :X  d   e[        T 5      " [        5      [!        [        TS[        T-
  -  -  5      5      :X  d   e[#        [$        U 4S j5        [        SS	S9m[#        [&        UU4S
 j5        [        SSS9m[#        [&        UU4S j5        [        SSS9m[#        [&        UU4S j5        g )Nr   Tr   r   r   r   r   c                     > [        T 5      $ r   r   r   s   r   r   test_levy.<locals>.<lambda>P  r   r   Fc                     > [        STT 5      $ r  rd   r   r   s   r   r   r  R      tC1~r   r   c                     > [        STT 5      $ r  r  r  s   r   r   r  U  r  r   c                     > [        STT 5      $ r  r  r  s   r   r   r  X  r  r   )r   rd   rG   r   r   r5   r   r@   r   r   r   r   r   r   r   rH   r*   r   r	  r   )r   r   r   s   @@@r   	test_levyr  G  s    	4	 BsT"AS"aA88??(2r"22221:a=DAbDN3r1a"f:+??!b&AEETUTZTZNA[\\\\q6!9T!QBZ.12222
 EF	5	!B
:-.s%A
:-.	4	 B
:-.r   c                  n   [        SSS9n [        SSS9n[        SX5      n[        U5      " [        5      U[        [        -  US-  U * [        [        5      -   S-  -   -  -  :X  d   e[        U5      " [        5      [        [        [        5      U -
  U-  5      [        -  [        R                  -   :X  d   eg )Nr   Tr   r   r   r   )
r   rf   r@   r   r   r   rH   r!   r   r   )r   r   r   s      r   test_logcauchyr  Z  s    	t	$B7T*E#r!A1:a=E1R4bS3q6\A4E)E#FGGGGq6!9c!frk501"4qvv====r   c                     [        SSS9n [        SSS9n[        SSS9n[        SX5      n[        U5      " [        5      [	        [
        U-  [        -  [        [        U -  [        -  5      -  [        [
        U-  [        -  5      -  [        [        S5      4S	5      :X  d   e[        U5      " [        5      [        [        * U -   U-  5      U[        [        * U -   U-  5      S
-   S-  -  -  :X  d   e[        U5      " [        5      S
[        U [        -
  U-  5      S
-   -  :X  d   e[        U5      " U5      X[        [        R                  * S
U-  -   5      -  -
  :X  d   eg )Nr   Tr   rr  r   r   r   r   r   r   r   )r   re   rI   r   r   r   r   r
   r   r   r@   rH   r   r   r   r   )r   rr  r   r   s       r   test_logisticr  d  s9   	4	 BsT"AsT"AbA #1%a(r!tAvc!B$q&k)$r!tAv,61aA9MO O O 1:a=C!b!,aqb2gq[1AA1E0I.IJJJJq6!93Qz?Q.////A;q>RC1$5"55555r   c            
        ^^ [        S5      u  mm[        STT5      (       d   e[        SSS9m[        SSS9m[        [        UU4S j5        [        SSS9m[        SSS9m[        [        UU4S	 j5        [        S
SS9u  mmp[        STT5      n[        U5      " U 5      TU T-  TS-
  -  -  TU T-  T-  S-   S-  -  -  :X  d   e[        U5      " U 5      SSU T-  T* -  -   -  :X  d   e[        U5      " U5      TUSU-
  -  ST-  -  -  :X  d   e[        U5      [        [        R                  TS:*  4[        T-  T[        [        T-  5      -  -  S45      :X  d   e[        SSS9m[        STT5      n[        U5      [        T-  T[        [        T-  5      -  -  :X  d   e[        SSS5      n[        U5      [        S5      :X  d   eg )Nr  r   r   Tr(  r   r   c                     > [        ST T5      $ r  rg   r   r   s   r   r   "test_loglogistic.<locals>.<lambda>y      {315r   c                     > [        ST T5      $ r  r  r  s   r   r   r  }  r  r   za b z pr   r   )prime)r   rg   r   r   r   r@   rH   r   r	   r   r   NaNr   r#   rE   r;   )r   r   r   r   r   s      @@r   test_loglogisticr  s  s   5>DAqsAq!!!!sT"AsT"A
:56sT"AsT"A
:56T2JAq!CAA1:a=Aqsa!en,a!A#A0A.ABBBBq6!91!r{?++++A;q>Q1q5	QqS11111 Q49aeeQ!V_r!tQs2a4y[/A4.HIIII4 ACAAQ42a43r!t9%%%%CAA!9	!$$$r   c            
         [        SSS9n [        SSS9n[        SX5      n[        S5      n[        U5      " U5      [        S5      [	        U * [        USU-
  -  5      -   S-  * SUS-  -  -  5      -  S[        [        5      -  U-  U-  SU-
  -  -  :X  d   e[        U5      " U5      [        [        S5      U * [        USU-
  -  5      -   -  SU-  -  5      S-  [        S5      S-  -   :X  d   eg )	Nr   Tr   rr  r   r   r   r   )
r   rh   r@   r   r   r   r   rH   r)   r   )r   rr  r   r   s       r   test_logitnormalr    s    	4	 BsT"ACAsA1:a=DGC2#Aq1uI*>)B(BAadF(K$LLaPTUWPXjYZl[\n^_bc^cNdeeeeq6!9DGbS3q!a%y>%9:AaC@A!Cad1fLLLLr   c            
      2  ^ [        SSS9n [        SSS9n[        SX5      m[        [        U4S j5        [        SSS9n[        SSS9n[        SX#5      m[	        T5      " [
        5      [        S5      [        U* [        [
        5      -   S-  * SUS-  -  -  5      -  S[
        -  [        [        5      -  U-  -  :X  d   e[        T5      " [
        5      [        [        [        S5      U* [        [
        5      -   -  SU-  -  5      S-  [        S	5      S-  -   [
        S
:  4S5      :X  d   e[        SS
S	5      m[	        T5      " [
        5      [        S5      [        [        [
        5      S-  * S-  5      -  S[
        -  [        [        5      -  -  :X  d   eg )Nr   Tr   r   r   r   c                     > [        T 5      $ r   r   r   s   r   r    test_lognormal.<locals>.<lambda>  r   r   r   r   r   r   )r   ri   r   r	  r@   r   r   r   r   r   rH   r   r)   r   )meanstdr   r   r   s       @r   test_lognormalr    s   $T"D
4
(C#t!A  EF	4	 B7T*E#r!A1:a=T!WSB3Q<!*;);&'qj*2 &3 345aCRL4FH I I I q6!9	T!WrcCFl3QuW=>q@A$q&!"#a%)*35 5 5 5 	#q!A1:a=DGCQ
1$55qs48|DDDDr   c            
        ^^ [        SSS9u  mm[        [        UU4S j5        [        SSS9u  mm[        [        UU4S j5        [        SSS9u  mm[        S	TT5      n U R                  R
                  R                  [        S
[        5      :X  d   e[        U 5      " [        5      TS[        T-  -   T* S-
  -  -  T-  :X  d   e[        U 5      " [        5      [        SS[        T-  -   T* -  -
  [        S
:  4S5      :X  d   eSm[        S	TT5      n [        U 5      TS-  :X  d   e[        U 5      [        TSS[!        SS5      -  -   -  5      :X  d   e[#        U 5      STS-  -  S-  :X  d   eg )Nza, lTr(  c                     > [        ST T5      $ Nr   r   r   rM  s   r   r   test_Lomax.<locals>.<lambda>      uS!Q/r   Fr   c                     > [        ST T5      $ r  r  r  s   r   r   r    r  r   r   r   r   r   r   r   r   r   r   )r   r   r   r   rG   r   r   r5   r   r@   r   rH   r   r	   rE   r;   r   rA   )r   r   rM  s    @@r   
test_Lomaxr    sV   6D)DAq
:/06&DAq
:/06D)DAqc1aA88??(1b/1111:a=Aq1Q3w1"q&11!3333q6!9	1AaCA2#6Q"?KKKK	Ac1aAQ41Q3;;!9	!R!Xa^*;%;"<====A;!AqD&("""r   c            	         [        SSS9n [        SU 5      n[        U5      " [        5      [	        S5      [        S-  -  [        [        S-  * SU S-  -  -  5      -  [	        [        5      U S-  -  -  :X  d   e[        U5      S[	        S5      -  U -  [	        [        5      -  :X  d   e[        U5      SU S-  -  [        -  SU S-  -  -   :X  d   e[        U5      " [        5      [        [	        S5      [        -  SU -  -  5      [	        S5      [        -  [        [        S-  * SU S-  -  -  5      -  [	        [        5      U -  -  -
  :X  d   e[        [        U5      " [        5      [        5      [        U5      " [        5      :X  d   eg )Nr   Tr   r   r   r   i)r   rj   r@   r   r   r   r   r	   rA   rH   r)   r   )r   r   s     r   test_maxwellr    sK   sT"AQA1:a=T!WQT\#q!teQq!tVn*==	b!Q$   Q41T!W9Q;tBx''''A;"QT'"*qAv----q6!9DGAIqsO,tAwqyadUAadF^9L/LdSUhWXj/YYYYYAq	1A...r   c            
        ^^ [        SSS9m[        SSS9m[        [        UU4S j5        [        SSS9m[        SSS9m[        [        UU4S	 j5        [        SSS9m[        S
TT5      n [	        U 5      " [
        5      [        S5      [        [        T[
        -
  T-  5      * S-  T* [
        -   ST-  -  -
  5      -  S[        [        5      -  T-  -  :X  d   e[        U 5      " [
        5      R                  5       S[        [        S5      [        T[
        -
  ST-  -  5      -  S-  5      -
  :X  d   e[        U 5      " [
        5      S[        * T-  [
        -  -  [        [        T-  [
        -  5      -  [        [        * T-  [
        -  [        SS5      -   5      -  [        [        5      -  :X  d   e[!        U 5      T["        T-  -   T[%        S5      -  -   :X  d   e['        U 5      " [
        5      ST* [
        -  -  [        T[
        -  5      -  [        T* [
        -  [        SS5      -   5      -  [        [        5      -  :X  d   eg )Nr   Fr   r   Tr   c                     > [        ST T5      $ NMrk   r   r   s   r   r   test_Moyal.<locals>.<lambda>      uSU3r   r(  c                     > [        ST T5      $ r  r  r  s   r   r   r    r  r   r  r   r   )r   r   r   rk   r@   r   r   r   r   rH   r6   r)   rI   r
   r-   r   r	   r   r   rJ   )r  r   r   s    @@r   
test_Moyalr    s   	%	 B7T*E
:34	4	 B7T*E
:347T*Ec2uA1:a=DGCb1fe^)<(<Q(>37QuW-). %/ /01$r(
50@B B B Bq6!91s473Q57I3J+J1+L'M#MMMM"1%a(A5
OC"QK,Gr%xzHQN:;-<<@H-E E E EQ42
5((5Q<7777%a(+qE6!8}SAY/Fvax(1a.890::>r(0C C C Cr   c            	      r   [        SSS9n [        SSS9n[        SX5      n[        U5      " [        5      S[        SU -  S-
  -  -  X -  -  X* -  -  [	        [        S-  * U -  U-  5      -  [        U 5      -  :X  d   e[        [        U5      5      [        U 5      [        U5      -  [        U [        R                  -   5      -  [        U S-   5      -  :X  d   e[        [        U5      5      X[        U [        R                  -   5      S-  -  [        U 5      [        U S-   5      -  -  -
  :X  d   e[        U5      " [        5      [        [        X [        S-  -  U-  5      [        U 5      -  [        S:  4S	5      :X  d   e[        SSS5      n[        U5      [!        [        [#        S5      5      5      :X  d   eg )
Nr   Tr   omegar   r   r   r   r   )r   rl   r@   r   r   r-   r6   r	   r   r   r   rA   rH   r   r.   rE   r;   r   )r   r  r   s      r   test_nakagamir    s   	t	$B7T*Eb A1:a=Qq1R4!8}_RV3ECL@!$adU2Xe^!455:2Y? @ @ @AaD>d2htE{2-22;-?@@Eb1fN O O OHQK 	%QVV$a''r5a=)@AAC C Cq6!9	!+B1a4!>uRy!H!a% P )+ + + + 	aA!9	$s1v,////r   c            	        ^^ [        S5      u  mm[        STT5      (       d   e[        S5      u  mmn [        STT5      n[        U5      " U 5      [	        S5      [	        TU S-  -  5      -  [        T* T* U -   S-  -  STS-  -  U -  -  5      -  S[	        [        5      -  -  :X  d   e[        SSS9u  mm[        SSS9n [        STT5      n[        U5      " U 5      [	        S5      [	        T5      -  [	        U S	-  5      -  [        T* T* U -   S-  -  STS-  -  U -  -  5      -  S[	        [        5      -  -  :X  d   e[        U5      T:X  d   e[        U5      R                  5       TS-  T-  :X  d   e[        U5      " U 5      [        R                  [        [	        S5      [	        T5      -  S
U T-  -   -  S[	        U 5      -  -  5      S-  -
  [        ST-  T-  5      -  [        [	        S5      [	        T5      -  SU T-  -   -  S[	        U 5      -  -  5      S-  -   [        R                  -   :X  d   e[        SSS9m[        [         UU4S j5        [        SSS9m[        SSS9m[        [         UU4S j5        g )Nr  r   za b zr   r   Tr   r   rY  r   r   r   r   c                     > [        ST T5      $ r  rn   r  s   r   r   'test_gaussian_inverse.<locals>.<lambda>      sAq9r   r   c                     > [        ST T5      $ r  r  r  s   r   r   r    r  r   )r   rn   r   r@   r   r   r   r   r	   rA   r   rH   r   r   r)   r   r   )r   r   r   r   s     @@r   test_gaussian_inverser    sj   5>DAq31%%%% gGAq!S!QA1:a=DGD1a4L0aR!a!^Qq!tVAX5N1OOQRSWXZS[Q[\\\\54(DAqsT"AQ"A1:a=DGDGODRM9#qb1"q&1naPQSTPTfUVh>W:XXZ[\`ac\dZdeeeeQ4199A;1a46)))q6!9#d1gd1goq1Q3w&?47&K"LQ"NNPSTUVWTWXYTYPZZ	T!WT!W_b1Q3h'473	4Q	679:@ @ @ @ 	&A
:9:d#A&A
:9:r   c                     [        SSS9u  pUS-   n[        SX5      n[        U5      n[        U5      " [        5      [        [        U* S-
  -  * XS-   -  -  S-   [        U :  4S5      :X  d   e[        U5      " [        5      [        * [        -  U -  US-   -  US-   -  [        U* S-
  [        * [        -  U -  5      -  :X  d   eU" [        5      [        US-   * -  X-  -  U-  :X  d   e[        [        U5      5      X -  US-
  -  :X  d   eg )Nzxm betaTr   r   r   r   r   )r   ro   r@   rH   r   r   rI   r
   r/   r6   r	   )xmr(   r   r   r  s        r   test_paretor    s$   y40HB1HEsBA1:D q6!9qD519~ob!8n4q8!r'BINO O O #1%a(RT"Wq!4!8,Z	A2a47-KKM M M 7aEAI,'3U;;;;AaD>UXuQw////r   c            	      $   Su  pUS-   n[        SX5      n[        U5      X -  [        US-
  5      -  :X  d   e[        U5      U S-  U-  [        US-
  S-  US-
  -  5      -  :X  d   e[	        U5      [        SS[        SS5      -  -  5      :X  d   eg )N)r   r   r   r   r   r   r      )ro   r	   r   rA   rE   r;   r   )r  r(   r   r   s       r   test_pareto_numericr  )  s    HB1HEsBAQ458AeaiL((((A;"a%+519q.%!)*D(EEEEE!9	!Ax1~$5"56666r   c                  *  ^^^ [        SSS9m[        SSS9u  mm[        [        UUU4S j5        [        SSS9u  mm[        [        UUU4S j5        [        SSS	9m[        SSS9u  mm[        [        U4S
 j5        [	        SSTT5      n [        U 5      " [        5      ST-  S[        -  -   T* T-   S-  -  :X  d   e[        U 5      " [        5      [        TS-  TS-  ST-  T-  -
  TS-  -   -  ST-  [        -  TS-  ST-  T-  -
  TS-  -   -  -
  [        S-  TS-  ST-  T-  -
  TS-  -   -  -   T[        :*  4S5      :X  d   e[	        SSSS5      n [        U 5      " [        5      S[        -  :X  d   e[        U 5      " [        5      [        [        S-  [        S:  4S5      :X  d   e[        U 5      [        SS5      :X  d   e[        U S:  5      S:X  d   e[        U S:  5      S:X  d   e[        U 5      [        S[        S5      -  5      :X  d   eg )Nr   Tr   za, br   c                      > [        STT T5      $ r  rp   r   r   r   s   r   r   $test_PowerFunction.<locals>.<lambda>7      c5!Q ?r   Fc                      > [        STT T5      $ r  r  r  s   r   r   r  :  r  r   r   c                      > [        ST SS5      $ )Nr   r   r   r  )r   s   r   r   r  >  r  r   r   r   r   r   r   r   r   )r   r   r   r   rp   r@   r   rH   r   r	   r   r>   rE   r;   r   )r   r   r   r   s    @@@r   test_PowerFunctionr  4  s   7-E6%DAq
J?@6&DAq
J?@7T*E6%DAq
J?@c1a#A1:a=RTAaCZ1"q&14444q6!9	1a4A!A1)<#=	!Aq!tac!e|ad"#$$&'dAqD1Q3q5L1a4,?&@$ABCq&#JKTV V V V 	c1a#A1:a=AaCq6!9	1a4a.(;;;;Q48Aa=   QU8q==QU8q==!9	!DG),,,,r   c            
      L   [        SSS9n [        SSS9n[        SX5      n[        U5      R                  R                  [        X-
  X-   5      :X  d   e[        U5      " [        5      [        [        [        * [        -  U -  U-  5      S-  [        [        [        * U-  5      4[        [        [        -  U -  U-  5      S-  [        [        [        U-  5      4[        S-  [        [        U -  [        -  5      -  [        U[        -  5      -  U[        -  US-  * [        S-  -  [        S-  -   -  -  S45      :X  d   e[        U5      " [        5      [        [        [        [        U -
  -  U-  5      S-   SU-  -  [!        [        X-   :*  X-
  [        :*  5      4S	5      :X  d   eg )
Nr   Tr   rr  r   r   r   r   r   )r   rr   rG   r   r   r5   rI   r   r   r   r
   r   r   r#   r@   r"   r3   )r   rr  r   s      r   test_raised_cosiner  M  s   	4	 BsT"AS" A!98BFBF#;;;;"1%a(c1"R%(1*oa'As1u6QrT"WQY9I2aQSTUQU;8WZ\^_Z_`cdefhdhijdj`kZklopqrspsltZtvwxyvy|}  @A  }A  |A  BC  EF  BF  |F  IK  MN  IN  |N  wO  [P  RV  ZW  XX X X 1:a=YRR[]);a)?!A#(Fa26k26Q;7(9:CE F F Fr   c                  b   [        SSS9n [        SU 5      n[        U5      " [        5      [	        S5      * [	        [
        5      -  U -  [        -  [        [	        S5      U -  [        -  S-  5      [        -
  -  [        U S-  * [        S-  -  S-  5      -  S-  S-   :X  d   e[        U5      " [        5      [        [        [        S-  * SU S-  -  -  5      -  U S-  -  :X  d   e[        U5      [	        S5      [	        [
        5      -  U -  S-  :X  d   e[        U5      [
        * U S-  -  S-  SU S-  -  -   :X  d   e[        U5      " [        5      S[        [        S-  * SU S-  -  -  5      -
  :X  d   e[        [        U5      " [        5      [        5      [        U5      " [        5      :X  d   eg )Nr   Tr   r   r   r   )r   rs   rI   r   r   r   r+   r
   r   r@   r	   rA   rH   r   )r   r   s     r   test_rayleighr  \  s   7T*EeA #1%a(d1gXd2h->u-DQ-FTRSWUZ][\_]^M^H_bcHc-dehjoqrjrirstvwswiwxyiyez-z{|-|  @A  .A  B  B  B1:a=QsAqD5!E1H*#566uax????Q44748#E)!++++A;2#eQh,q.1UAX:5555q6!9CAqz 233333Aq	1A...r   c            	      X  ^^ [        SSS9m[        SSS9m[        STT5      n [        U 5      " [        5      S[        [	        T5      * [	        T5      -   -  -  :X  d   e[        U 5      " [        5      [        [	        T5      [	        T5      [	        T5      -
  -  [	        [        5      [	        T5      [	        T5      -
  -  -
  T[        :*  4S5      :X  d   e[        SSS	5      n [        U 5      S
[	        S	5      [	        S5      -
  -  :X  d   e[        U S:  5      [        R                  :X  d   e[        U S:  5      [	        S5      [	        S	5      [	        S5      -
  -  [	        S5      [	        S	5      [	        S5      -
  -  -
  :X  d   e[        U 5      " S5      [	        S5      [	        S	5      [	        S5      -
  -  [	        S5      [	        S	5      [	        S5      -
  -  -
  :X  d   e[        SSS9m[        [        UU4S j5        [        SSS9m[        SSS9m[        [        UU4S j5        g )Nr   Tr   r   r   r   r   r      r   r      r   r   c                     > [        ST T5      $ r  rt   r  s   r   r   !test_reciprocal.<locals>.<lambda>y  s    z#q!4r   r   c                  $   > [        ST T-   T 5      $ r  r  r  s   r   r   r  }  s    z#q1ua8r   )r   rt   r@   r   r   rH   r   r	   r>   r   Zeror   r   r   )r   r   r   s    @@r   test_reciprocalr  j  s   sAsA31A1:a=Aq3q6'CF"234444q6!9	3q63q6CF?#;c!fc!fsSTvo>V#VXY]^X^"_ajkkkk32AQ42s2wQ'((((QU8qvvQV9B3r7SV#34s1vR3q6AQ7RRRRRq6":RCGc!f$45A#b'CPQFBR8SSSSS&A
:45d#Ad#A
:89r   c            	         [        SSS9n [        SSS9n[        SX5      n[        U5      " [        5      XS[	        U * [        -  5      -
  -  S-   -  [	        U * [        -  5      -  [	        U* [	        U * [        -  5      -  5      -  :X  d   eg r  )r   ru   r@   r   r   r  s      r   test_shiftedgompertzr
    s    sT"A

&CQ$A1:a=AAQBqD	M2Q67QBqD	A#sd3PQrRSt9nBUUUUUr   c            
        ^ [        SSS9n [        SU 5      m[        T5      " [        5      S[        S-  U -  -   U * S-  [        R
                  -
  -  [        U 5      [        [        R
                  U S-  5      -  -  :X  d   e[        T5      " [        5      [        R
                  [        [        U S-  [        R
                  -   5      -  [        [        R
                  U S-  [        R
                  -   4[        SS5      4[        S-  * U -  5      -  [        [        5      [        U 5      -  [        U S-  5      -  -  -   :X  d   e[        [        U4S j5        g )	NnuTr   r   r   r   r   c                     > [        T 5      $ r   r   r   s   r   r   test_studentt.<locals>.<lambda>  r   r   )r   rv   r@   r   r   r   r   r(   rH   r-   r1   r   r   r   r	  )r  r   s    @r   test_studenttr    s    	t	$BbA1:a=QAb[RCEAFFN;T"Xd166SUVWSWFX=XYYYYq6!95A#7!7qvvr!taff}>U!)!Q 1AqD589= "=>B2htBx>OPUVXYZVZP[>["] ] ] ] ]
 EFr   c            	         [        SSS9n [        SSS9n[        SSS9n[        SSS9n[        SXX#5      n[        U5      " [        5      [	        SU -  S	[        -  -   U * U-   U * U-
  U-   U-   -  -  U [        :*  [        U:  -  4S	U * U-
  U-   U-   -  U[        :*  [        U:  -  4S	U-  S	[        -  -
  U* U-   U * U-
  U-   U-   -  -  U[        :*  [        U:*  -  4S
5      :X  d   e[        SSSS	S5      n[        U5      [        SS	5      :X  d   e[        U5      [        SS5      :X  d   e[        US	:  5      [        SS5      :X  d   e[        U5      [        [        SS	5      5      :X  d   eg )Nr   Tr   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   rw   r@   r   r   r	   r   rA   r>   rE   r;   )r   r   r   r   r   s        r   test_trapezoidalr    s   sAsAsAsACq$A1:a=I1qs
qb1frAvzA~5N'ORSWXRX]^ab]bQc&d'(1"q&1*q.'9AFq1u;M&N()!ac	aR!Vqb1fqj1n4M'NQRVWQW\]ab\bPc&d&/1 1 1 1
 	CAq!$AQ48Aq>!!!A;(1b/)))QU8x1~%%%!9	(1a.1111r   c                     [        S5      n [        S5      n[        S5      n[        SXU5      n[        U5      R                  R                  [        X5      :X  d   e[        [        U5      " [        5      5      S:X  d   e[        U5      " [        5      R                  5       SU * U-   -  [        U[        -  5      -  SU * U-   -  [        U[        -  5      -  -   SX-
  -  [        U [        -  5      -  -   [        S-  U * U-   -  U * U-   -  X-
  -  -  R                  5       :X  d   e[        [        U5      " [        5      5      S:X  d   eg )	Nr   r   r   r   zPiecewise(((-2*a + 2*x)/((-a + b)*(-a + c)), (a <= x) & (c > x)), (2/(-a + b), Eq(c, x)), ((2*b - 2*x)/((-a + b)*(b - c)), (b >= x) & (c < x)), (0, True))r   r   zg(2*(-a + b)*exp(I*c*x) - 2*(-a + c)*exp(I*b*x) - 2*(b - c)*exp(I*a*x))/(x**2*(-a + b)*(-a + c)*(b - c)))r   rx   rG   r   r   r5   r   r@   r   rJ   r   r   rI   )r   r   r   r   s       r   test_triangularr    sJ   sAsAsA3a A!98A>111wqz!} #_ ` ` ` &a(+2241"q&k#ac(QQZAaC001ae9S1X3EE1qbSTfXYWY\]W]H^`a`eHfgooqr r r&q)!,-mn n nr   c            	         [        SSS9n [        SSS9n[        SX5      n[        SSS5      n[        U5      R                  R                  [        X5      :X  d   e[        U5      " S5      S[        S5      -  S	[        S5      -  -   :X  d   e[        U5      " S5      S
[        S5      -  S-  S[        S5      -  S-  -   :X  d   e[        U5      " S5      S[        -  SS[        -  -   -  [        [        [        S[        -  5      -  5      -  :X  d   e[        U5      " [        5      [        S[        U S-  -
  US-  -
  S-  -  U * U-   S-  -  [        [        U:*  U [        :*  5      4S5      :X  d   eg )Nr   Tr   r   r   r   r   i   ir      r   r   r   r   )r   rq   rG   r   r   r5   rJ   r   rI   r
   r@   r   r   r3   )r   r   r   r   s       r   test_quadratic_ur    s[   sAsA3A31A!98A>111%a(+CF
RAY0FFFF%a(+r#a&y{RAYq[/HHHH"1%a(AaCacN3qQqSz?,JJJJ1:a=YA!GacMA+=(=rAvk(Ia1fa1f-(/09; < < <r   c                  p   [        SSS9n [        SSS9n[        SX U-   5      n[        U5      XS-  -   :X  d   e[        U5      R	                  5       US-  S-  :X  d   e[        SS	S
5      n[        US	:  5      S:X  a  [        US
:  5      S:X  d   e[        US:  5      [        US:  5      s=:X  a  [        R                  :X  d   e   e[        U5      [        S5      :X  d   e[        S5      n[        U5      " U5      nUR                  US5      [        R                  :X  d   eUR                  US5      S:X  d   eUR                  US5      S:X  d   e[        U5      nU" S5      S:X  a  U" S	5      S:X  d   eU" [        SS5      5      [        SS5      :X  d   eU" S
5      S:X  a  U" S5      S:X  d   eg )NrM  Tr   wr   r   r   r   r   r   r   r   r   g@r   rX  r  r   )r   ry   r	   rA   r   r>   r   r   rE   r;   r@   r   rH   r   )rM  r  r   r   r   r   s         r   test_uniformr    s   sAsT"AQAAQ41s7??A;1a47*** 	QAQU8q=Qq1uX]**QU8qQx)166)))))!9	!$$$sA
1A66!S>QVV###66!R=A66!Q<1AAQ4191""Xa^A...Q4191""r   c                      [        SSS9n [        SSS9n[        SX U-   5      n[        X :  5      S:X  a  [        X U-   :  5      S:X  d   eg)	au  This stopped working because SingleContinuousPSpace.compute_density no
longer calls integrate on a DiracDelta but rather just solves directly.
integrate used to call UniformDistribution.expectation which special-cased
subsed out the Min and Max terms that Uniform produces

I decided to regress on this class for general cleanliness (and I suspect
speed) of the algorithm.
rM  Tr   r  r   r   r   N)r   ry   r>   )rM  r  r   s      r   test_uniform_Pr    sS     	sAsT"AQAAQU8q=Qqq5y\Q....r   c                  R   [        SSS9n [        S5      n[        S5      n[        SU 5      n[        SU-  U* U-   U S-
  -  -  [	        X5      -  US[        U5      45      [        U S-
  5      -  n[        U5      " U5      R                  U5      (       d   eUR                  R                  R                  [        SU 5      :X  d   e[        U5      " U5      [        * [        [        U-  5      S-
  -  U-  U -  :X  d   e[!        U5      " U5      [        U5      S-
  U-  U -  :X  d   eg )	Nrj  TrA  r   r   r   r   r   )r   r   rz   r   r   r   r   r@   r  rG   r   r   r5   rI   r
   r   rJ   )rj  r  r   r   r  s        r   test_uniformsumr    s   sD!A	sBsA3A
rBha1q5))(1/9B58;L
MiXY\]X]N^
^C1:a=!!#&&&& 88??(1a.000 #1%a(aRQqSA->q-@1,DDDD &a(+Q!Q/BBBBr   c                      [        S5      n [        SSS9n[        SX5      n[        U5      " [        5      [	        U[        [        U -
  5      -  5      S[        -  [        SU5      -  -  :X  d   eg )Nr   r   Tr   r   r   r   )r   r{   r@   r   r   r"   r   r%   )r   r   r   s      r   test_von_misesr      s^    	BsT"AbA1:a=C#a"f+."WQ]0BCCCCr   c                     [        SSS9u  p[        SX5      n[        U5      R                  5       U [	        SSU-  -   5      -  :X  d   e[        U5      R                  5       U S-  [	        SSU-  -   5      -  [        U5      S-  -
  R                  5       :X  d   e[        [        U5      5      S[	        SSU-  -   5      S-  -  S[	        SSU-  -   5      -  [	        SSU-  -   5      -  -
  [	        SSU-  -   5      -   [	        SSU-  -   5      S-  * [	        SSU-  -   5      -   [        SS5      -  -  :X  d   e[        [        U5      5      S[	        SSU-  -   5      S	-  -  S
[	        SSU-  -   5      S-  -  [	        SSU-  -   5      -  -   S	[	        SSU-  -   5      -  [	        SSU-  -   5      -  -
  [	        SS	U-  -   5      -   [	        SSU-  -   5      S-  [	        SSU-  -   5      -
  S-  -  :X  d   eg )Nr  Tr   r   r   r   r   rY  r   rX  )
r   r|   r	   r   r-   rA   r6   rC   r   rD   r   s      r   test_weibullr"    s   54(DA 	QAQ4;;=Aa!A#g....A;AqD5QqS>$9AaD!G$C#K#K#MMMMHQK QuQ1W~q'8%81U1qs7^;KERSVWXYVYRYN;Z%Z]bcdghijgjcj]k%kotuvyz{|y|u|o}  @A  pA  oA  DI  JK  NO  PQ  NQ  JQ  DR  oR  U]  ^_  ab  Uc  nc  %c  c  c  cHQK Ra!A#g(9%9	%AaC.!
E!ac'N*&+-.uQ1W~-=eA!Gn-L&MOTUVYZ[\Y\U\~&^`efgjklmjmfm`npq`qtyz{~  AB  B  {B  uC  aC  FG  `G%G G G Gr   c                     Sn [         R                  S[        SS5      S/nU H  n[        SX5      n[	        [        U5      5      [        U [        SS[        U5      -  -   5      -  5      :X  d   e[	        [        U5      5      [	        U S-  [        SS[        U5      -  -   5      -  [        U5      S-  -
  5      :X  a  M   e   g )Nr   r   r   r   r   )	r   r   r   r|   r6   r	   r   r-   rA   )r   bvalsr   r   s       r   test_weibull_numericr%    s    	AVVQA*EC!~Qq1QqT6z1B-B!CCCC$qD5QqtV$$qtQw.)0 0 	0 0 r   c            	         [        SSS9n [        SU 5      n[        U5      R                  R                  [        U * U 5      :X  d   e[        U5      " [        5      S[        [        S-  * U S-  -   5      -  [        U S-  -  -  :X  d   e[        U5      S:X  d   e[        U5      " [        5      [        S[        SU [        -  5      -  U [        -  -  [        [        S5      4S5      :X  d   eg )	NRTr   r   r   r   r   r   )r   r~   rG   r   r   r5   r@   r   r   r   r	   rI   r   r&   r   )r'  r   s     r   test_wignersemicircler(  !  s    sT"Aa A!98QB?2221:a=AdAqD51a4<00"QT'::::Q4199 #1%a(a1Q3'1-r!Qx8)DE E Er   c                    ^^^^ [        S5      u  p[        SSS9u  mn[        SSSS9u  mm[        [        S 5        [        [        UU4S	 j5        [        S
U T5        [        [        U4S j5        [	        ST5        [
        [        [        [        4 H9  m[        [        UUU4S j5        [        [        UUU4S j5        T" STU5        M;     g )Nr  zp qTr   zm nFr  c                      [        SSS5      $ )Nr   r   r   rm   r   r   r   r   -test_input_value_assertions.<locals>.<lambda>4  s    vc1a0r   c                     > [        ST T5      $ r  r+  )rq  rj  s   r   r   r,  5  s    vc1a0r   r   c                     > [        ST 5      $ r  )rY   )rq  s   r   r   r,  7  s    {32r   Exc                     > T " STT5      $ r  r   )fnrq  r   s   r   r   r,  :      2c1a=r   c                     > T " STT5      $ r  r   )r1  rj  r   s   r   r   r,  ;  r2  r   r   )	r   r   r   rm   rY   ro   r|   rN   r^   )r   r   qr1  rq  rj  r   s      @@@@r   test_input_value_assertionsr5  /  s    5>DA54(DAq55t4DAq
:01
:01
31
:23awe,z01z01
31 -r   c                  6   [        SSS5      n [        S5      n[        [        S5      U-  [	        US-  * S-  5      -  S[        [
        5      -  -  U[        * [        45      n[        [        S5      [	        US-  * S-  5      -  S[        [
        5      -  -  US[        45      n[        [        5         [        U SS9R                  [        5      R                  U5      (       d   e[        U S-   SS9R                  [        5      R                  US-   5      (       d   e[        U S:  SS9R                  [        5      R                  U5      (       d   e S S S 5        [        U S:  U S-  S:  5      [        R                  :X  d   eg ! , (       d  f       N8= f)Nr   r   r   r   r   Fr|  )rm   r   r2   r   r   r   r   r   r  r	   r   r  r>   r   r   )r   r   expr1expr2s       r   test_unevaluatedr9  ?  sO   sAqAc
AT!WQYsAqD57|+QtBxZ81rc2,GET!WS!Q$q\)1T"X:6Ar
CE		%U#++H5>>uEEEEQ'//9BB519MMMMQ'//9BB5IIII 
&
 QUAqD1H''' 
&	%s   4B#F


Fc                      [        SSS5      n [        [        5         [        [	        U S:  SS95      [
        :X  d   e S S S 5        g ! , (       d  f       g = f)NTr  r   !   Fr|  )rm   r   r  typer>   r   )r;  s    r   test_probability_unevaluatedr>  L  sB    sBA		%Aa"fu-.+=== 
&	%	%s   !A
Ac                      [        SSS5      n [        SSS5      n[        [        X-   SS9" [        5      [        5      (       d   eg )Nr   r   r   r   r   Fr|  )rm   r  r@   r   r2   r   s     r   test_density_unevaluatedr@  R  s?    sAqAsAqAgacE215x@@@@r   c                     [        SS5      n [        S5      nU R                  U5      [        [	        S5      U-  S-  5      S-  [
        R                  -   :X  d   eU R                  SU5      S:X  d   eU R                  X5      S:X  d   eU R                  US-  U5      S:X  d   e[        U[        SS5      5      n[        S5      n[        [	        S5      [        US-
  S-  * S-  5      -  S[	        [        5      -  -  U[        * S45      nUR                  US:  S	S
9R                  U5      SL d   e[        [	        S5      [        US-
  S-  * S-  5      -  S[	        [        5      -  -  US[        45      nUR                  US:  S	S
9R                  U5      SL d   e[        U[        SS5      5      n[        [	        S5      [        US-
  S-  * S-  5      -  S[	        [        5      -  -  US[        45      nUR                  US:  S	S
9R                  U5      SL d   e[        [	        S5      [        US-
  S-  * S-  5      -  S[	        [        5      -  -  U[        * S45      nUR                  US:  S	S
9R                  U5      SL d   eg )Nr   r   r   r   r   r{      r4  Fr|  Trz     r  rX  )r   r   rH   r)   r   r   r   expectationr   r   r2   r   r   r   r  r  )	ndr   r   r{  r  r  r   	expected3	expected4s	            r   test_NormalDistributionrH  X  sd   	Aq	!BsA66!9DGAIaK(*QVV3333>>!Q1$$$>>!1$$$>>!Q$"a'''q"4Q":;A	tBarAvk\"_!55qbzBBQ<PI==Q=/88CtKKKarAvk\"_!55qbzBB2;OI==Q=/88CtKKKq"4Q":;AarAvk\#%5!6648Db!R[QI==Q=/88CtKKKarAvk\#%5!6648Db2#q\RI==Q=/88CtKKKr   c                     [        SSS5      n [        SU S5      n[        USS9" [        5      (       d   e[        [	        U5      [
        5      (       d   e[        SSS/SS	/S	S//5      n[        [	        U5      R                  [        5      (       d   e[        U5      " [        5      R                  5       [        S
5      [        [        S-  * S-  [        S
-  -   [        S5      S
-  -
  5      -  S[        [        5      -  -  :X  d   eg )Nr   r   r   r;  r   Fr|  r   r   r   r  r   )rm   r@   r   r  rG   r   r  r   r6   r   r   r   r   )r   measr   s      r   test_random_parametersrK  r  s    	a	B#r1D4%(++++fTlN3333sQFaVaV,-AfQi,,.LMMMM4=$$&$q'#q!teBh1nqtAv6M2N*NPRSWXZS[P[*\\\\r   c                      [        SSS5      n [        SU S5      n[        U[        U S5      5      [        SSS5      :X  d   eg )Nr   r   r   r;  r   r   )rm   rF   r   )r   rJ  s     r   test_random_parameters_givenrM  |  sB    	a	B#r1Dr"ay!VCA%6666r   c                      [        SSS5      n [        SU S5      n[        [        [        U [	        U[
        5      SS9" [        5      5      [        5      (       d   eg )Nr   r   r   r   r   Fr|  )rm   r  r6   r@   r   r   r   r   )r   r   s     r   test_conjugate_priorsrO    sS    	a	BsBAhwr2a8eDQGH   r   c                      [        SSS5      n [        U S-  5      (       d   e[        [        U S-  5      5      (       d   e[        [        U 5      5      (       d   eg)zSince using solve in place of deltaintegrate we're able to perform
substantially more complex density computations on single continuous random
variables r   r   r   r   r   N)rm   r@   r   r   )r   s    r   test_difficult_univariaterQ    sO     	sAqA1a4===3q!t93q6???r   c                      [        SS5      n [        SSS5      n[        U S:  5      [        R                  L d   e[        US:  5      [        R                  L d   eg )Nr   r   gr   r   r   )rY   r^   r>   r   r  )r   Gs     r   test_issue_10003rU    sP    CAc1aAQV9QV9r   c                     [        SSS9n [        SSS9n[        SSS9u  p#n[        SSSS9n[        S	X5      [        S
X45      [        SU5      [	        SU5      /nU Hn  n[        U5      " U 5      [        UR                  R                  R                  5       " U 5      5      -
  n[        UR                  [        5      5      nUS:X  a  Mn   e   g )Nr   Tr   r   zsigma xm alphar   rj  rC  r   r>   Cr	   r   )r   rm   ro   rS   rY   rH   r6   rG   r@   compute_cdfr   r*   )	r   r   r   r  r   rj  distribsr   compdiffs	            r   test_precomputed_cdfr[    s    $A	D	!B/$?EuTD1A3"3"sAU#	H q6!9x(8(8(D(D(Fq(IJJH,,T231}} r   c                  X  ^ SS K mU4S jn U " [        SSS5      SS5        U " [        SS5      STR                  5        U " [	        SS5      STR                  5        U " [        SS	5      STR                  5        U " [        S
SS5      TR                  * TR                  5        U " [        SSS5      TR                  * TR                  5        U " [        SSS5      SS5        U " [        SS5      STR                  5        U " [        SSS5      SS5        U " [        SS5      SS5        g )Nr   c                   >^^^
 [        U 5      n[        S5      n[        U/[        U 5      " U5      S5      n[        [        U/U" [        5      [        [        [        -  U-  5      -  S5      m
U
UUU4S jnS H_  nU" U5      nU" U5      n	[        [        U5      [        U	5      -
  5      S:  d   e[        [        U5      [        U	5      -
  5      S:  a  M_   e   g )Nr   mpmathc                 6   >^  TR                  UU 4S jTT/SS9$ )Nc                    > T" U T5      $ r   r   )r   r   r   s    r   r   ^test_precomputed_characteristic_functions.<locals>.test_cf.<locals>.<lambda>.<locals>.<lambda>  s    a1gr   r   )	maxdegree)quad)r   r   r^  support_lower_limitsupport_upper_limits   `r   r   Ltest_precomputed_characteristic_functions.<locals>.test_cf.<locals>.<lambda>  s    $58KM`7amopr   )r   r   r4     g-q=)
r@   r   r7   rI   r   r   r
   absr   r   )distrd  re  r   r   cf1cf2
test_pointn1n2r   r^  s    ``       @r   test_cf:test_precomputed_characteristic_functions.<locals>.test_cf  s    dm3K s3D9!<hG aVSVC!AJ.9p (JZBZBr"v2'%///r"v2'%/// (r   r   r   r   r   r   r   rX  rM  rj  r   r   rr   g      ?rs  r  rY  )r^  rN   rR   infrS   rY   re   rm   rr   rs   ry   r~   )ro  r^  s    @r   )test_precomputed_characteristic_functionsrs    s    0& DaOQ"CQKFJJ'JsA6::.KQFJJ/HS!Q&**fjj9F3AVZZ8La#Q*HS#6::.GCQQ'S!$b!,r   c                  
   [        SSS9n [        SSS5      [        SSS	S
5      [        SSS5      [	        SSSS5      [        SSS5      [        SS
S5      [        SSS5      [        SSS5      [        SSS5      [        SSS5      [        SS5      /nU HS  n[        S5       HA  n[        [        [        U5      " U 5      U 5      [!        U5      " U 5      U SSSSS9(       a  MA   e   MU     [#        SS5      n[!        U5      " U 5      R%                  ['        U 5      S5      R)                  5       n[        US S!9" U 5      R%                  ['        U 5      S5      R)                  5       n[        [        X`5      XPSSSSS9(       d   eg )"Nr   Tr   Ar   rz  Dr   r   r   r	      r   Fr   rX  rY  rT  r  GIKr4  LAr   iNr   r   r   )r   r   r   r   USFr|  )r   rL   rU   rW   r]   r^   r_   rb   rc   re   rl   rv   rangetnr   rH   r@   rz   r   r   r   )r   rY  distr_r}  pdf01cdf01s          r   test_long_precomputed_cdfr    sh   $A3A#q"a 3ACAr"#q!q!$Q"D"a S"a S!QS!H qAd3u:a=!,genQ.?a1PQUVWWWW   
D!	BBKNa!,113EU#A&++E!Ha8==?Ed5ne!qA;;;r   c                      [        SSS5      n [        X [        R                  :  5      [	        SS5      :X  d   e[        X S:  5      [        R                  :X  d   eg )Nr   r   r   r   r   )ry   r	   r   r   r   r   s    r   test_issue_13324r    sK    QAQAFF
x1~---QA;!&&   r   c                      [        SSS5      n [        SSS5      n[        X-  5      [        R                  :X  d   e[        XS-   S-
  -  5      [        R                  :X  d   e[        XU S-   -  X -  -
  -  5      [        R                  :X  d   eg )Nr   r   r   r   )ry   r	   r   r  r   s     r   test_issue_20756r    s    RARAQU8qvvQq5A+166)))QQU)ac/"#qvv---r   c                  .   [        SS5      n [        SSS5      n[        [        U S5      5      [        R
                  L d   e[        [        US5      5      [        R
                  L d   e[        [        U[        5      5      [        R
                  L d   eg )Nr	   r   r|  r   r  r   r   )rY   rm   r>   r   r   r  r   )r	   r|  s     r   test_FiniteSet_probr    sp    CAsAqAR1X;!&&   R1X;!&&   R1X;!&&   r   c                  J   [        SS5      n [        SS5      n[        [        U S5      5      S:X  d   e[        [        US5      5      S:X  d   e[        [        US5      5      S:X  d   e[        [        US5      5      S:X  d   e[        [        U [        5      5      S:X  d   eg )Nr	   r   r   r   r   r   )rY   rS   r>   r   r   )r	   r   s     r   test_prob_neqr    s    CA3AR1X;!R1X;!R1X;!R1X;!R1X;!r   c                     [        SSS5      n [        [        U S-  U -
  S:  5      5      [        [	        S5      5      * S-  [        [	        S5      S-  5      S-  -
  [        SS5      -   :X  d   e[        [        U S-  S-
  S:  5      5      [        S[	        S5      -  S-  5      * S-  [        [	        S5      S-  5      S-  -
  [        SS5      -   :X  d   eg )Nr|  r   r   r   r   r   )rm   r6   r>   r)   r   r*   r   r|  s    r   
test_unionr    s    sAqAAadQhlO$	T!Wa$tAwqy/!++hq!n<= = =AadQhlO$	QtAwYq[	!d4719oa//(1a.@A A Ar   c            	         [        SSS5      n [        [        [        U S:  U S:  5      5      5      [	        [        S5      5      * S-  [        [        S5      S-  5      S-  -
  [        SS5      -   :X  d   e[        [        U S:  U S:  5      5      [        U S:  5      :X  d   e[        [        U S:  U S:  5      5      S:X  d   eg )Nr|  r   r   r   r   )rm   r6   r>   r4   r)   r   r*   r   r  s    r   test_Orr    s    sAqAAbQA&'(	T!Wa$tAwqy/!++hq!n<= = =RAq1u!AE(***RAq1u!###r   c                  0   [        SS5      n [        [        U S5      [        U S5      5      S:X  d   e[        [        U S5      [        U S5      5      S:X  d   e[        U S:  [        U S5      5      S:X  d   e[        U S:  [        U S5      5      S:X  d   eg )Nr	   r   r   r   )rY   r>   r   )r	   s    r   test_conditional_eqr    s    CAR1Xr!Qx A%%%R1Xr!Qx A%%%QUBq!H"""QUBq!H"""r   c                     [        S5      n [        S5      n[        U [        [        R
                  SU :*  U S:  -  4SU S:  U S:  -  4[        R
                  U S:  U S:  -  4S5      5      n[        U[        SS5      S9n[        X5      nUR                  [        U [        [	        S5      S-  U S:  U S:  -  4SU S:  U S:  -  4[	        S5      S-  U S:  U S:  -  4S5      5      :X  d   e[        UR                  5      [        SS5      :X  d   e[        UR                  5      [        SS5      :X  d   e[        UR                  5      [        S	S
5      :X  d   eg )Nr   r   r   r   r   r   r   r      r   )r   r   r   r   r   r   r   r5   r   r   rE   valuer	   r   rA   )r   r   r  spaces       r   #test_ContinuousDistributionHandmader    sX   sAc
A!YA!5AqD1Q3<7H	
!Q$1	+ ,D)$HQNCD"1+E88vaAaDFQ!VA4F+G	
Q!VA!A$q&16a!e*<!=y"J K K K K%++(1a.000U[[>Xa^+++EKK HR$4444r   c                  b   ^  [        [        [        SS5      5      m [        [        U 4S j5        g )Nr   r   c                  V   > [         R                  " T [        S-   [        [        15      $ r   )r   r   r   r   r  s   r   r   "test_issue_16318.<locals>.<lambda>+  s     5II!QqSSTVWRXYr   )r   r   r5   r   r   r  s   @r   test_issue_16318r  (  s     q(1a.1A
:YZr   c                  `   ^  [        SS[        S5      S-  5      m [        [        U 4S j5        g )Nr   r   r   r   c                  &   > [        T S-  T -   5      $ )Nr   )r@   r   s   r   r   &test_compute_density.<locals>.<lambda>/  s    wq!tax0r   )rm   r   r   r   r   s   @r   test_compute_densityr  -  s%    sAvg)*A
:01r   N(  sympy.concrete.summationsr   sympy.core.functionr   r   r   sympy.core.mulr   
sympy.corer   rJ  r	   r   r
   r   r   sympy.core.relationalr   r   sympy.core.singletonr   sympy.core.symbolr   r   r   (sympy.functions.combinatorial.factorialsr   r   $sympy.functions.elementary.complexesr   r   r   r   &sympy.functions.elementary.exponentialr   r   %sympy.functions.elementary.hyperbolicr   r   #sympy.functions.elementary.integersr   (sympy.functions.elementary.miscellaneousr   $sympy.functions.elementary.piecewiser   (sympy.functions.elementary.trigonometricr    r!   r"   r#   r$   sympy.functions.special.besselr%   r&   r'   &sympy.functions.special.beta_functionsr(   'sympy.functions.special.error_functionsr)   r*   r+   r,   'sympy.functions.special.gamma_functionsr-   r.   r/   &sympy.functions.special.zeta_functionsr0   sympy.functions.special.hyperr1   sympy.integrals.integralsr2   sympy.logic.boolalgr3   r4   sympy.sets.setsr5   sympy.simplify.simplifyr6   sympy.utilities.lambdifyr7   r8   r:   r;   r<   r=   sympy.statsr>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   sympy.stats.crv_typesr   r   r   sympy.stats.joint_rv_typesr   r   sympy.stats.crvr   r   sympy.stats.compound_rvr    sympy.stats.symbolic_probabilityr   sympy.testing.pytestr   r   r   r   sympy.core.randomr   r  Infinityr   mapr   r   r   r   r   r   r   r   r   r   r   r   r   r
  r  r  r&  r5  r?  rK  rU  r_  rh  rm  ro  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  r   r"  r%  r(  r5  r9  r>  r@  rH  rK  rM  rO  rQ  rU  r[  rs  r  r  r  r  r  r  r  r  r  r  r  r   r   r   <module>r     s0   ) ; ;  ! 8 8 * " 6 6 J D D = > 5 9 : P P F F 7 M M S S 7 / . ) $ , - : 1 ? ?
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/ n m f J 2 8 E E 6ZZ
fe
1a72
	296'*?,+@HV70
2@01$=B%$6(&&,*9(3,%.-*<2 )2 )2V2;0JQ / /<G/M+O/&>6%4ME4#$
/ C C*0";80.7-2F/:*VG2$n <"#4 /  /C&DG0E 
(>AL4]7$ - -D<2!
.!A$#5[
2r   