a
    lhL                     @   s~  d dl mZ d dlmZmZmZ d dlmZ d dlm	Z	 d dl
mZmZmZmZ d dlmZmZ d dlmZ d dlmZmZmZ d d	lmZmZ d d
lmZmZmZm Z  d dl!m"Z"m#Z# d dl$m%Z%m&Z& d dl'm(Z( d dl)m*Z* d dl+m,Z, d dl-m.Z.m/Z/m0Z0m1Z1m2Z2 d dl3m4Z4m5Z5m6Z6 d dl7m8Z8 d dl9m:Z:m;Z;m<Z<m=Z= d dl>m?Z?m@Z@mAZA d dlBmCZC d dlDmEZE d dlFmGZG d dlHmIZImJZJ d dlKmLZL d dlMmNZN d dlOmPZP d dl9mQZQ d dlDmRZR d dlKmSZSmTZTmUZU d dlVmWZWmZmXZXmYZYmZZZm[Z[m\Z\m]Z]m^Z^m_Z_m`Z`maZambZbmcZcmdZdmeZemfZfmgZgmhZhmiZimjZjmkZkmlZlmmZmmnZnmoZompZpmqZqmrZrmsZsmtZtmuZumvZvmwZwmxZxmyZymzZzm{Z{m|Z|m}Z}m~Z~mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZ d d lmZmZmZ d d!lmZmZ d d"lmZmZ d d#lmZ d d$lmZ d d%lmZmZmZmZ d d&lmZ ejZeed'\ZZZd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Zd4d5 Zd6d7 Zd8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM ZdNdO ZdPdQ ZdRdS ZdTdU ZedVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Zed`da Zdbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo Zdpdq Zdrds Zdtdu Zdvdw Zdxdy Zdzd{ Zed|d} Zd~d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zeedd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Z dd Zdd Zdd Zdd Zdd Zedd Zdd Zdd ZddÄ Z	ddń Z
ddǄ ZddɄ Zdd˄ Zdd̈́ Zddτ Zddф Zddӄ ZdS )    )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_numericallyZxyzc               	   C   s  t ddd} t ddd}tddd}|| |  }t|| ks@J t||d	 ksTJ t|}t ddd}||d	tj t||  d	  d	|d	    d	ttj  |  ksJ t	|d	 dk t
d	tj d	 ksJ t||}|ttttd	| td	|  d	|  td	| d   tt tt| ks6J t|t|| | ksPJ t|tdksfJ |jd dksJ d S )
NmuTrealsigmapositivexr         )r   rl   r   r@   r?   r   Halfr   r   r=   r(   r   r;   r<   r:   r   r7   r4   oor   rD   rF   compute_expectationdoit)r   r   XYpdfr   Zans r   R/var/www/auris/lib/python3.9/site-packages/sympy/stats/tests/test_continuous_rv.pytest_single_normal7   s.    8&.
r   c                  C   s   t ddd} t| | dk}td}t||dt| | ksBJ |jjjtdtksZJ t	|t
dt
t ksvJ t	| d t	|d ksJ d S )Nr   r   r   zr   )rl   rE   r   r?   rF   domainsetr4   r   r   r   r   )r   r   r   r   r   r   test_conditional_1dP   s     r   c                     s   t ddd t d dkjtddks,J t d dkj jksHJ tt d dk dkjtddksrJ tt fdd t  dk} | j	j
jtdtksJ d S )Nr   r   r   r   c                      s   t t dkS Nr   )r>   r"   r   r   r   r   <lambda>b       z'test_ContinuousDomain.<locals>.<lambda>)rl   r>   r   r4   symbolr2   r   
ValueErrorrE   rF   r   r   )r   r   r   r   test_ContinuousDomain]   s     *r   c                  C   s2  t dddt ddd } }tddd}t| | dks:J t| | dksNJ t| |  d	ksbJ t| |dkstJ td|  | |  d
t|  ksJ t| dksJ t| | dksJ t| dksJ t| | dksJ t| |dksJ t| | | t| | | ksJ t| ddks(J t	| ddks<J t| | d	dksTJ t	| dt| kslJ t
| |  ddksJ t
| | dt| | ksJ t
| | d	t| | ksJ t| t| | ddksJ t| t| | dtjksJ t| |tdtd| tj  ks.J d S )Nr   r   r   ypTr   r            )rl   r   r   r@   rA   rB   rC   r   r   r   r   r   r   r   r   r   r7   One)r   r   r   r   r   r   test_multiple_normali   s.    $"   r   c                  C   sp  t ddd\} }t ddd\}}tddd}td| |}td||}td	|}t d
dd\}}	}
t|| kspJ t|| | | ksJ t|| |	 |t| |	 ksJ t||d ksJ t|||  |	 t||d t|  ksJ t|d| ksJ t|| |	 |t| |	 ks,J t|||  |	 | ||  |	 ksVJ t|t| kslJ d S )Nzmu1 mu2Tr   zsigma1 sigma2r   lambdar   r   r   a b cr   r   )r   r   rl   rX   r   r@   rD   r:   )Zmu1Zmu2s1s2rater   r   Zabcr   r   r   test_symbolic   s     
$0&*r   c                     s   t ddd t } t dk | dtks2J | dtjksDJ t  dk} | ddksbJ tddt} | ddksJ tdkd| d ksJ tt	 fdd	 td
d}t|}|t
tdtt
  t
dkfdksJ d S )Nr   r   r   r   
   r   c                      s   t   S N)rG   r   r   r   r   r   r      r   ztest_cdf.<locals>.<lambda>r   r   T)rl   rG   r=   rewriter)   r   r   rX   r   r   r   r   r   )dr   fr   r   r   test_cdf   s    

r   c                  C   s  t ddd} t| }|dt dtt  ks2J tddd}t|}|ddksVJ |dtttj kspJ tdd}t|}|ddksJ |d t	dd	td d	  ksJ t
ddd} t| }|ddksJ |dtdtdd
t   ksJ tdddd} t| }|ddks*J |ddt tt	dd
 d
 ksRJ tddd}t|}|ddksxJ |dttd
 tt  ksJ d S )Nr   r   r   r   r   r            r   )rx   rH   r	   r   rl   r   r   rX   expandr
   rm   r   rW   rc   )r   cfr   r   Lr   r   r   test_characteristic_function   s.    
&&(r   c                  C   s

  t ddd} t d\}}}ttd||| }|t|f|| f| ksJJ ttd|| }|td|  t|d tj  t|d tj ft	ddf| d d  t|d  t|d ftjf| d d  ksJ tt
d|| }|dd|   | d  ksJ ttd||| }|d| |  |  ks6J ttd|||| }|t||  |d | d  d  d| |   ksJ ttd|| }||||   ksJ ttd||| }|| |  d |  ksJ ttd||| }|t||  t| |  d  ksJ ttd||| }||t| t| | | ksPJ ttd||| }|t||  |d  | d  d  ksJ ttd||| }|t||  t| |  d ||  d  ksJ ttd||| }|t||  |d | d  d  ksJ ttd||| }||| |  |  t| | |   ksVJ ttd||| }t|d	ks|J ttd||| }|td t||   t||   ||  |d | d  td    ksJ ttd|| }|tdtt | |  ttd| |  d d  t|d | d  d  d d ksJJ tt d|||| }t|d
ksrJ tt!d||| }|t||   t||   | | |   ksJ tt"d|| }|t| d |  | ksJ tt#d|| }|dt$d||   ||   ksJ ttddd| }|%| &| dtdddd ksZJ ttdd| }|%| &| dtdtdt	ddftj tt tt	ddft	ddftj dtd tdt	ddftj dtt   ksJ tt
dd| }|%| &| dt'ks$J ttddd| }|%| &| ddksTJ ttdddd| }|%| &| dtd ksJ ttdd| }|%| &| ddksJ ttddd| }|%| &| ddksJ ttddd| }|%| &| dt(d ksJ ttddd| }|%| &| dt) t*ddd ks\J ttddd| }|%| &| ddksJ ttddd| }|%| &| dtddksJ ttddd| }|%| &| dttjksJ ttddd| }|%| &| dtddks.J ttddd| }|%| &| ddt) dtd  ksnJ ttddd| }|%| &| ddt) td  td dtd  d  t)td  t+d dtd    ksJ ttdd| }|%| &| dtdtt d k	s J tt dddd| }|%| &| dt) td k	s\J tt!ddd| }|%| &| ddk	sJ tt"dd| }|%| &| ddk	sJ tt#dd| }|%| &| ddt$dd t$dd t$dd k
sJ d S )NtTr   r   r   r   r   r   zk(3*(t*(-4*b + (a + b)**2) + 4)*exp(b*t) - 3*(t*(a**2 + 2*a*(b - 2) + b**2) + 4)*exp(a*t))/(t**2*(a - b)**3)zb(-2*(-a + b)*exp(c*t) + 2*(-a + c)*exp(b*t) + 2*(b - c)*exp(a*t))/(t**2*(-a + b)*(-a + c)*(b - c)))r   )r   )r   r   r   )r   )r   r   ))r   r   r   r   ir   ),r   rI   rM   r0   rQ   r   r,   r   r   r
   rR   rV   rW   r   rX   r]   r`   r_   r+   rb   rd   r'   rl   rn   r.   rp   strrq   r   r   rr   r(   rw   rx   ry   r}   r$   r   subsr	   r   er9   r   )r   r   r   r   Zmgfr   r   r   test_moment_generating_function   s    &

 6($,2*.J42$(,
" """,&,&&r   c                  C   sx  t dttd  d  dt t  } tt| dd}tddd}t|t|ksTJ t|dkt|dkkspJ tttt t	dt
d}|jjjt	dt
ksJ t|dksJ t|dktd	ksJ ttd
d  tddd\}}}dt|||   ||d   t| |  } t|| t	dt
d}td||}t|t|  dksVJ t|t|  dkstJ d S )Nr   T)checkr   r   r   r   r   r   c                   S   s   t ttt tddddS )Nr   r   T)r   r   )rJ   r   r   r4   r   r   r   r   r   f  r   z#test_ContinuousRV.<locals>.<lambda>z	x k thetar   )r   r   r   r   rJ   rl   r@   r=   r   r4   r   rF   r   r   r   r   r   r   r,   r]   r5   )r   r   r   r   _xkthetar   r   r   test_ContinuousRVZ  s     &.r   c               	   C   s   t ddd} t ddd}td| |}t|tdttt | t|     ksRJ t|ttd| tkfdtt|  t |  |   t |tkfd	ksJ t	|j
jt| |ksJ d S )
Nr   Tr   r   r   r   r   r   r   T)r   rK   r?   r   r   r   rG   r   r   rF   r   r   r4   r   r   r   r   r   r   test_arcsinr  s    .*
r   c                      sP  t dddt dddt dddtd t tt d tt  t  t tt  tt d    ksJ t jjt	t
ksJ tt fdd	 t ddd
ttfdd	 t ddd
ttfdd	 t dddttfdd	 t dddt ddd
ttfdd	 d S )NalphaTr   r'   r   r   r   c                      s   t  S r   rI   r   r   r   r   r     r   ztest_benini.<locals>.<lambda>nonpositivec                      s   t d S Nr   rL   r   r   r'   r   r   r   r     r   c                      s   t d S r   r   r   r   r   r   r     r   c                      s   t d S r   r   r   r   r   r   r     r   c                      s   t d S r   r   r   r   r   r   r     r   )r   rL   r?   r   r   r   rF   r   r   r4   r   r   NotImplementedErrorr   r   r   )r   r   r'   r   r   test_benini~  s$    ((
r   c                  C   s  t ddd\} }td| |}t|jjtddks6J t|tt| f| | ft	t ks^J t
|tt| d  dt |d   t| | ksJ tt|| | |  ksJ tt|| | | d d| d  |  | d  d|  |d   d|  |  |d  |d   ksJ d	\} }td| |}tt|| t| |  ksLJ tt|| | t| | d | | d   ksJ t|tddtd  ksJ d S )
Nz
alpha betaTr   r   r   r   r   r   )r   r   )r   rM   rF   r   r   r4   rH   r   r0   r	   r?   r'   r5   r   r@   r   r   rD   r:   r   )r   r   Br   r   r   	test_beta  s    (6f"6r   c                     s~  t ddd\ tdddtd} td }t|jjtdd	ksLJ t|}td
}t	||   d	  d |   d	| d	   t
 d  t|   t|   | dtf}|||sJ t d\ td sJ tdddd tt fdd tddd tddddtt fdd tddd tdddtddddtt fdd d S )Na bTr   r   )nonnegativer   r   r   r   r   r   r   r   Fr   r   c                      s   t d S r   rN   r   r   r   r   r   r   r     r   z&test_beta_noncentral.<locals>.<lambda>r   c                      s   t d S r   r   r   r   r   r   r     r   )r   r   c                      s   t d S r   r   r   r   r   r   r     r   )r   r   r   rN   rF   r   r   r4   r?   r   r   r'   r   r   dummy_eqr   r   )_kr   densr   resr   r   r   test_beta_noncentral  s0    :r   c                     s   t ddd t dddtd } t| tt d  td      t  ks\J t ddd tt fdd	 t ddd t dddtt fd
d	 tddd} t| tdksJ d S )Nr   Tr   r'   r   r   r   c                      s   t d S r   rO   r   r   Zbetapr   r   r     r   z test_betaprime.<locals>.<lambda>c                      s   t d S r   r   r   r   r   r   r     r   )	r   rO   r?   r   r'   r   r   rD   r:   r   r   r   r   test_betaprime  s    8r   c                     s  t ddd\ tt fdd t ddd\ tt fdd t ddd	\ tt fd
d tdd } | jjjt ksJ t| t	dd  t	d dd  d     ksJ t
| t	t d  d  t	d  d d     d  d d    t	kfdks,J t|  d      ksRJ tdddd} t|  tdkszJ t| ttddksJ t|  ddtdd   ksJ d S )NzL, HTnegativec                      s   t dd S Nr   r   r   r   Hr   r   r   r     r   z$test_BoundedPareto.<locals>.<lambda>Fr   c                      s   t dd S r   r   r   r   r   r   r     r   r   c                      s   t dd S )Nr   r   r   r   r   r   r   r     r   r   r   r   r   r   r         )r   r   r   r   rF   r   r   r4   r?   r   rG   r   r   r5   r   rD   r:   r
   r@   r   r   r   r   test_BoundedPareto  s*    84&r  c                     sJ  t dddt dddt ddd} td t tt tt tt   ks^J tt fdd	 t	 td
t
 d
t d d     ksJ tt ttt	 tksJ t | tt
| tj    ksJ t dddttfdd	 t dddttfdd	 t tksFJ d S )Nx0Tr   r,   r   r   r   c                      s   t  S r   r   r   r   r   r   r     r   ztest_cauchy.<locals>.<lambda>r   r   x1Fc                      s   t d S r   rP   r   )r,   r  r   r   r     r   r   c                      s   t d S r   r  r   )r,   r  r   r   r     r   )r   rP   rH   r   r   r   r	   r   r   r?   r   r   rG   r   r#   r   r   r   rD   r:   )r   r   )r   r,   r  r  r   test_cauchy  s    .4"*r  c                     s  ddl m}  tddd td }t|td  d d  t d   ttd  d  t d  ksnJ t|tt	d|  t t d t
dd   t d t
dd  ft
d	d ftd  d  t d  t d ft
dd ftd  d  ksJ t|tt	dt t d t
dd   t d t
dd  ft
d	d ftd d  t d  t d ft
dd ftd d  ksJ tddd
d tt fdd tdd
dd tt fdd d S )Nr   )r	   r   Tintegerr   r   r   r   Fr	  r   c                      s
   t d S r   rQ   r   r   r   r   r     r   ztest_chi.<locals>.<lambda>c                      s
   t d S r   r  r   r  r   r   r     r   )sympy.core.numbersr	   r   rQ   r?   r   r   r,   rH   r   r   r0   rI   r   r   )r	   r   r   r  r   test_chi  s,    
LF
$B
"r  c                     s  t ddd t dtd } t| tt   t   d   ttd  d d d   t d d t  ksJ t dddd	 tt fd
d t dddd	 t dddtt fdd t ddd t dddtt fdd d S )Nr   Tr  lr   r   r   Fr
  c                      s   t d S r   rS   r   r   r  r   r   r      r   z%test_chi_noncentral.<locals>.<lambda>r   c                      s   t d S r   r  r   r  r   r   r   $  r   r   c                      s   t d S r   r  r   r  r   r   r   (  r   )r   rS   r?   r   r   r$   r   r   r   r   r  r   test_chi_noncentral  s     &
r  c                     s~  t ddd td } t| tdt t d   d  ks@J t| td  d  t d d   tt d  t d  ksJ t| tt	t
 d td t d  tdkfd	ksJ t|  ksJ t| d  ksJ tdd
} t| ddtd ttdd dtt  ttdd  ks:J t dddd tt fdd t dddd tt fdd d S )Nr   Tr  r   r   r   r   r   r      r   i   i  Fr
  c                      s
   t d S r   rR   r   r  r   r   r   ;  r   z"test_chi_squared.<locals>.<lambda>c                      s
   t d S r   r  r   r  r   r   r   >  r   )r   rR   rH   r   r	   r?   r   r,   rG   r   r-   r   r@   r   r
   r   r(   r   r   r   r   r  r   test_chi_squared+  s    
*H<
Hr  c                     sT  t dddt dddt ddd td } t| t  t     t   d  d   t ksxJ t| ttdt       tdkfd	ksJ t ddd
tt fdd t dddt ddd
tt fdd t dddt ddd
 tt fdd tdddd} t| t	dksPJ d S )Nr   Tr   r   r   r   r   r   r   r   c                      s   t d S r   rT   r   r   r   r   r   r   r   L  r   ztest_dagum.<locals>.<lambda>c                      s   t d S r   r  r   r  r   r   r   P  r   c                      s   t d S r   r  r   r  r   r   r   T  r   )
r   rT   r?   r   rG   r   r   r   rD   r:   r   r   r  r   
test_dagumA  s$    F*
r  c                  C   s   t ddd} t ddd}t ddd}td| ||}| | t| d|   }t| t|  d t|t|  }t|t|| ksJ d S )	Nr   Tr   nr   r   r   r   )r   rU   r   r   r,   r/   r?   )r   r  r   r   ZdividendZdivisorr   r   r   
test_davisX  s    $r  c                  C   s   t dddd} t ddd}td| |}t|tt| d  ||   tt |  t|  ks`J t|ttt| |t t|  tdkfd	ksJ d S )
Nr   Tr
  r  r   r   r   r   r   )	r   rV   r?   r   r   r,   rG   r   r-   )r   r  r   r   r   r   test_erlangc  s    :(r  c            
      C   s  t d\} }t ddd\}}td| ||}t|||t|||d  d|   d|   d  ttd||d  |  |  d|   d ksJ |||   }|| }ttdd||}ttd|d ||}|t| |d d  t|  }	t|||	ks
J t	|
 |d |d  ks,J t|
 d|d	 |d  t|d |d   |t|d |d     ks~J d S )
Nzm, zzs, lTr   r   r   r   r   r   )r   rW   r?   r   r)   r   rG   rl   r   r@   r   rB   )
mr   sr  r   uvZGaussianCDF1ZGaussianCDF2Zactual_outputr   r   r   test_exgaussianm  s$    4&
""0r"  c            
   	   C   sR  t ddd} td| }t dddd}t|d|  ks8J t|d| d  ksPJ t|dks`J t|t|d	ksvJ t|d
ksJ t|t|dksJ td| dt|dksJ t|d	d| d	  ksJ t|dkt	j
u sJ t|dkt|  ksJ t|dktd|  ks"J t||td|  |  ksFJ t|dkjtddksdJ tdd}t|ttdksJ td}t||kt| |  ksJ t||k dksJ t d}td}t|td}tt tdtd|  |d	tf}|j|d	kddt|s.J tdtd|  |ddf}	|j|dk ddt|	snJ W d    n1 s0    Y  tdd|  }t|||t|ksJ t||| |  |d|  |  dtddd| d    tddd| d      ksJ t|d|  || |d|  |d	ktdtd
d ksNJ d S )Nr   Tr   r   r   r   r   r   r   	   r   r  r   r   ir   r   _zr   Fevaluate   U   ) r   rX   r   r@   rB   r   rC   r   r=   r   r   r   r   r   r>   r   r4   rD   r:   r   r   r   r   UserWarningr1   r   probabilityr   r   r|   r   r
   )
r   r   r   r   r   r   r$  r   	expected1	expected2r   r   r   test_exponential  sJ    
$
 
$D2
$r-  c                  C   s   t d} t d}t ddd}t ddd}td| ||}t|||tt| | | |   d| td	|   ksxJ t||tjt	d	| t| | | | t
|  |  dtd	|    ksJ d S )
Nr   r   r   Tr   r'   r   r   r   )r   rY   r?   r   r   r,   rG   r   r   r-   r   )r   r   r   r'   r   r   r   r   test_exponential_power  s"    
r.  c                      s  t dddt dddtd t td  tt  t       ttd d   ks|J tt fdd t ddd	ttfd
d t ddddttfdd t dddt ddd	ttfdd t ddddttfdd d S )Nd1Tr   d2r   r   c                      s   t  S r   r   r   r   r   r   r     r   z%test_f_distribution.<locals>.<lambda>r   c                      s   t d  S r   rZ   r   r/  r   r   r     r   F)r   r	  c                      s   t d  S r   r1  r   r2  r   r   r     r   c                      s   t d S r   r1  r   r/  r0  r   r   r     r   c                      s   t d S r   r1  r   r3  r   r   r     r   )	r   rZ   r?   r   r   r'   r   r   r   r   r   )r   r/  r0  r   test_f_distribution  s     :
r4  c                  C   s   t ddd} t ddd}td| |}t|td| | d   ||d   | tdt  | |  d |d    t| t  t| d |d  ksJ d S )Nr/  Tr   r0  r   r   )r   r[   r?   r   r   r'   )r/  r0  r   r   r   r   test_fisher_z  s    6
r5  c                  C   s   t ddd} t ddd}t ddd}td| ||d}t|t| t| | |  d	   tt| | |     | kszJ t|ttt| t | |    |tkfd
ksJ d S )Nr   Tr   r  r  r   r   )r  r  r   r   )r   r\   r?   r   r   rG   r   )r   r  r  r   r   r   r   test_frechet  s    Fr6  c                  C   s  t ddd} t ddd}td| |}t|tt | t d |   ksLJ t|tt| d  ||    tt |  t|  ksJ t|ddt	t
|  t| d t| d  | t| t	|  t| d   t	dkfd	ksJ t|t|dksJ td
dd\} }td| |}t|| | ks,J t|| |d  ksFJ t| dt|  ksdJ t| dd|   ksJ tdd|  d| }t||| | | | |  dd|    t|  | ddd|    dd|     t| d d t|d d   ksJ d S )Nr   Tr   r   r   r   r8   r   r   zk thetar   r   r  r   i r      )r   r]   rH   r   r	   r?   r   r,   rG   r   r   r-   r   r   r   r@   rB   r   r   rC   r|   r5   )r   r   r   r   r   r   r   
test_gamma  s4    (<
4r8  c                     s   t ddd} t ddd}td| | t tt|  d  ||   t| t  t|  ks`J t ttt| |t t|  tdkfdksJ t	 td	t
 | t | d	   t| d	t| tt
 t   t|  ksJ tt fd
d d S )Nr   Tr   r   r   r   r   r   r   c                      s   t  S r   r   r   r   r   r   r     r   z$test_gamma_inverse.<locals>.<lambda>)r   r^   r?   r   r   r,   rG   r   r.   rH   r	   r&   r   r   r   r   r   r   r   r   test_gamma_inverse	  s    <4"
r:  c                  C   s   t ddd} t ddd}td| |}t|t| | t| t| t  t| t| t   ksfJ t|tdt|t| t| t    ksJ tt|ttt|tksJ d S Nr   Tr   etar   r   )r   r_   r?   r   r   rG   r   r   r<  r   r   r   r   test_gompertz  s    B2r>  c                  C   sV  t ddd} t d}t d}t d}td| |}td| |dd}t|| t||  t| |   tt||   t| |    |  ksJ t|| t| |  t||   tt| |   t||    |  ksJ t|| tt||   t| |   ksJ t||tt| | tt |  | d  ksRJ d S )	Nr'   Tr   r   r   r   )Zminimumr   )	r   r`   r?   r   r   rG   rH   r	   r,   )r'   r   r   r   r   r   r   r   r   test_gumbel  s     <<
r?  c                  C   s   t ddd} t ddd}td| |}t|tt| d  |  | t|   d |d   ks^J t|ttdtdk ft|   d |  d tdkfdksJ d S )	Nr   Tr   r   r   r   r   r   )r   ra   r?   r   rG   r   r   r   r   r   test_kumaraswamy-  s    :r@  c                  C   s  t d} t ddd}td| |}t|ttt|  t |d td  d  ksTJ t|tttt|   | d|  ksJ t|tt	t|  t | d | tkft| t |  d d dfksJ tdddgddgddgg}t
t|jtsJ d S )	Nr   r   Tr   r   r   r   r   )r   rb   rH   r   r   r	   r?   r   rG   r   
isinstancerF   distributionr   )r   r   r   r   r   r   test_laplace8  s    4.(
rC  c                      s$  t dddt dddtd  jjjttks<J t tt	dt
  t dt    t tjtj   ksJ t ttt	dt   ksJ tt fdd	 t dd
dttfdd	 t dddttfdd	 t dddttfdd	 d S )Nr   Tr   r   r   r   r   c                      s   t  S r   r   r   r   r   r   r   P  r   ztest_levy.<locals>.<lambda>Fc                      s   t d S r   rc   r   r   r   r   r   r   R  r   r   c                      s   t d S r   rD  r   rE  r   r   r   U  r   c                      s   t d S r   rD  r   rE  r   r   r   X  r   )r   rc   rF   r   r   r4   r   r?   r   r   r   r   r   r   r   rG   r)   r   r   r   r   r   )r   r   r   r   	test_levyG  s    J(rF  c                  C   s   t ddd} t ddd}td| |}t|t|tt |d |  tt d    ksZJ t|tttt|  | t tj	 ksJ d S )Nr   Tr   r   r   r   )
r   re   r?   r   r   r   rG   r    r   r   )r   r   r   r   r   r   test_logcauchyZ  s
    6rG  c                  C   s  t ddd} t ddd}t ddd}td| |}t|ttt| t tt|  t  tt| t  t	tdfd	ks|J t
|ttt |  | |tt |  | d
 d   ksJ t|td
t| t | d
  ksJ t||| |ttj d
|    ksJ d S )Nr   Tr   r  r   r   r   r   r   r   r   )r   rd   rH   r   r   r   r   r	   r   r   r?   rG   r   r   r   r   )r   r  r   r   r   r   r   test_logisticd  s    
:@(rH  c                     s  t d\ td sJ tddd tdddtt fdd	 tddd tdddtt fd
d	 t ddd\ } }td }t|| |   d    |    d d   ksJ t|| dd|       ksJ t|| |d|  d   ks J t|t	t
jdkft  tt   dfksZJ t dddtd }t|t  tt   ksJ tddd}t|tdksJ d S )Nr   r   r   Tr   r   r   c                      s   t d S r   rf   r   r9  r   r   r   y  r   z"test_loglogistic.<locals>.<lambda>c                      s   t d S r   rI  r   r9  r   r   r   }  r   za b z pr   r   )prime)r   rf   r   r   r   r?   rG   r   r   r   r   NaNr   r"   rD   r:   )r   r   r   r   r9  r   test_loglogistics  s&    <&*:&rL  c                  C   s   t ddd} t ddd}td| |}t d}t||tdt|  t|d|   d  d|d    dtt | | d|   ksJ t||ttd|  t|d|    d|  d t	dd  ksJ d S )	Nr   Tr   r  r   r   r   r   )
r   rg   r?   r   r   r   r   rG   r(   r   )r   r  r   r   r   r   r   test_logitnormal  s    `rM  c                     sJ  t ddd} t ddd}td| | tt fdd t ddd}t ddd}td|| t ttd	t| tt d	  d	|d	    d	t tt	 |  ksJ t
 ttttd	| tt  d	|  d	 td
d	  tdkfdksJ tddd
 t ttd	tttd	  d	  d	t tt	  ksFJ d S )Nr   Tr   r   r   r   c                      s   t  S r   r   r   r   r   r   r     r   z test_lognormal.<locals>.<lambda>r   r   r   r   )r   rh   r   r   r?   r   r   r   r   r   rG   r   r(   r   )meanZstdr   r   r   r   r   test_lognormal  s,    $

$

rO  c                     sN  t ddd\ tt fdd t ddd\ tt fdd t ddd	\ td
 } | jjjtdtks|J t	| t
 dt
    d    ksJ t| t
tddt
      t
dkfdksJ d td
 } t| d ksJ t| tddtdd   ks,J t| dd  d ksJJ d S )Nza, lTr   c                      s   t d S Nr   r   r   r   r  r   r   r     r   ztest_Lomax.<locals>.<lambda>Fr   c                      s   t d S rP  rQ  r   rR  r   r   r     r   r   r   r   r   r   r   r   r   r   )r   r   r   r   rF   r   r   r4   r   r?   r   rG   r   r   rD   r:   r
   r@   r   r   rR  r   
test_Lomax  s    .4(rS  c                  C   s0  t ddd} td| }t|ttdtd  ttd  d| d    tt| d   ks`J t|dtd |  tt ksJ t|d| d  t d| d   ksJ t	|tt
tdt d|   tdt ttd  d| d    tt|    ksJ tt	|ttt|tks,J d S )Nr   Tr   r   r   r   i)r   ri   r?   r   r   r   r   r   r@   rG   r(   r   )r   r   r   r   r   test_maxwell  s    
2
$(\rT  c                     s  t ddd t dddtt fdd t ddd t ddd	tt fd
d t dddtd } t| ttdtt t   d   t d    dtt   ksJ t	| t
 dttdt t d   d  ksJ t| tdt  t  tt  t  tt  t tdd  tt ksZJ t|  t  td  ksJ t| td t  t t  t t tdd  tt ksJ d S )Nr   Fr   r   Tr   c                      s   t d S NMrj   r   r   r   r   r   r     r   ztest_Moyal.<locals>.<lambda>r   c                      s   t d S rU  rW  r   rX  r   r   r     r   rV  r   r   )r   r   r   rj   r?   r   r   r   r   rG   r5   r(   rH   r	   r,   r
   r   r   r   rI   )rV  r   rX  r   
test_Moyal  s2    &
>*&"rY  c                  C   s\  t ddd} t ddd}td| |}t|tdtd|  d   | |   ||    ttd  |  |  t|  ksxJ tt|t| t| t| t	j
  t| d  ksJ tt|||t| t	j
 d  t| t| d    ksJ t|ttt| | td  | t|  tdkfd	ks.J tddd}t|tttdksXJ d S )
Nr   Tr   omegar   r   r   r   r   )r   rk   r?   r   r   r,   r5   r   r   r   r   r@   rG   r   r-   rD   r:   r   )r   rZ  r   r   r   r   test_nakagami  s,    .



,$r[  c                     s*  t d\ td sJ t d\ } td }t|| tdt| d   t   |  d  d d  |    dtt  ksJ t ddd\ tddd} td }t|| tdt t| d	  t   |  d  d d  |    dtt  ksJ t| ks.J t	|
  d  ksLJ t|| tjttdt d
|     dt|   d  td    ttdt d|     dt|   d  tj ksJ t ddd tt fdd t ddd t dddtt fdd d S )Nr   r   za b zr   r   Tr   r   r  r   r   r   r   c                      s   t d S r   rm   r   r9  r   r   r     r   z'test_gaussian_inverse.<locals>.<lambda>r   c                      s   t d S r   r\  r   r9  r   r   r     r   )r   rm   r~   r?   r   r   r   r   r   r@   r   rG   r   r   r(   r   r   )r   r   r   r9  r   test_gaussian_inverse  s*    \bN.r]  c                  C   s   t ddd\} }|d }td| |}t|}t|ttt| d   | |d   d t| kfdksjJ t|tt t |  |d  |d  t| d t t |   ksJ |tt|d   | |  | ksJ t	t
|||  |d  ksJ d S )Nzxm betaTr   r   r   r   r   )r   rn   r?   rG   r   r   rH   r	   r.   r5   r   )xmr'   r   r   r   r   r   r   test_pareto  s    
,
6&r_  c                  C   s   d\} }|d }t d| |}t|||  t|d  ks<J t|| d | t|d d |d   kslJ t|tddtdd  ksJ d S )N)r   r   r   r   r   r   r      )rn   r   r   r@   rD   r:   r
   )r^  r'   r   r   r   r   r   test_pareto_numeric)  s     0ra  c                     s  t dddtddd\ tt fdd tddd\ tt fd	d t ddd
tddd\ ttfdd tdd } t| td  dt     d  ksJ t| tt d  d d    d   d  t  d d    d    td  d d    d     tkfdksRJ tdddd} t| tdt kszJ t| tttd tdkfdksJ t	| t
ddksJ t| dk dksJ t| dk dksJ t| tdtd ksJ d S )Nr   Tr   za, br   c                      s   t d S r   ro   r   r   r   r   r   r   r   7  r   z$test_PowerFunction.<locals>.<lambda>Fc                      s   t d S r   rb  r   rc  r   r   r   :  r   r   c                      s   t d ddS )Nr   r   r   rb  r   )r   r   r   r   >  r   r   r   r   r   r   r   r   )r   r   r   r   ro   r?   r   rG   r   r   r
   r=   rD   r:   r   r   r   rc  r   test_PowerFunction4  s4    ..&"(rd  c               	   C   sF  t ddd} t ddd}td| |}t|jjt| | | | ksFJ t|ttt	t
 t |  | d ttt | ft	t
t |  | d ttt| ftd t	t
|  t  t|t  |t |d  td  td    dfksJ t|ttttt|   | d d|  tt| | k| | tkfd	ksBJ d S )
Nr   Tr   r  r   r   r   r   r   )r   rq   rF   r   r   r4   rH   r   r   r   r	   r   r   r"   r?   r!   r2   )r   r  r   r   r   r   test_raised_cosineM  s    "
*re  c                  C   s\  t ddd} td| }t|ttd tt |  t ttd|  t d t  t| d  td  d  d d ks~J t	|ttttd  d| d    | d  ksJ t
|tdtt |  d ksJ t|t | d  d d| d   ksJ t|tdttd  d| d    ks4J tt|ttt	|tksXJ d S )Nr   Tr   r   r   r   )r   rr   rH   r   r   r   r*   r	   r   r?   r   r@   rG   r   )r   r   r   r   r   test_rayleigh\  s    
h6$,0rf  c                     s  t ddd t dddtd } t| tdtt  t   ksNJ t| ttt t t  ttt t    tkfdksJ tddd	} t| d
td	td  ksJ t| dk t	j
ksJ t| dk tdtd	td  tdtd	td   ks J t| dtdtd	td  tdtd	td   ksbJ tddd tt fdd tddd tdddtt fdd d S )Nr   Tr   r   r   r   r   r      r   r      r   r   c                      s   t d S r   rs   r   r9  r   r   r   y  r   z!test_reciprocal.<locals>.<lambda>r   c                      s   t d   S r   ri  r   r9  r   r   r   }  r   )r   rs   r?   r   r   rG   r   r   r=   r   Zeror   r   r   r   r   r9  r   test_reciprocalj  s    *N BBrk  c                  C   s|   t ddd} t ddd}td| |}t|t| |dt|  t   d  t|  t  t| t|  t   ksxJ d S r;  )r   rt   r?   r   r   r=  r   r   r   test_shiftedgompertz  s    rl  c                     s   t ddd} td|  t tdtd |   |  d tj  t| ttj| d   ks^J t ttjtt	| d tj  t
tj| d tj ftddftd  |   ttt|  t	| d    ksJ tt fdd	 d S )
NnuTr   r   r   r   r   c                      s   t  S r   r   r   r   r   r   r     r   ztest_studentt.<locals>.<lambda>)r   ru   r?   r   r   r   r   r'   rG   r,   r0   r
   r   r   r   )rm  r   r   r   test_studentt  s    
H6rn  c                  C   sl  t ddd} t ddd}t ddd}t ddd}td| |||}t|ttd|  d	t  |  | |  | | |   | tkt|k @ fd	|  | | |  |tkt|k @ fd	| d	t  | | |  | | |   |tkt|k@ fd
ksJ tdddd	d}t|tdd	ksJ t|tddks0J t|d	k tddksLJ t	|t
tdd	kshJ d S )Nr   Tr   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   rv   r?   r   r   r   r
   r@   r=   rD   r:   )r   r   r   r   r   r   r   r   test_trapezoidal  s    F$:
ro  c                  C   s   t d} t d}t d}td| ||}t|jjt| |ks@J tt|tdksXJ t	|t
 d|  |  t|t  d|  |  t|t   d||  t| t   td |  |  |  |  ||   
 ksJ tt|tdksJ d S )	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   rw   rF   r   r   r4   r   r?   r   rI   r   r   rH   )r   r   r   r   r   r   r   test_triangular  s    rrp  c                  C   s2  t ddd} t ddd}td| |}tddd}t|jjt| |ksJJ t|ddtd d	td  ksrJ t|dd
td d dtd d  ksJ t|ddt	 ddt	   tt	tdt	   ksJ t
|ttdt| d  |d  d  |  | d  tt|k| tkfdks.J d S )Nr   Tr   r   r   r   r   i   ir      r   r   r   r   )r   rp   rF   r   r   r4   rI   r   rH   r	   r?   r   r   r2   )r   r   r   r   r   r   r   test_quadratic_u  s    (084rs  c                  C   s  t ddd} t ddd}td| | | }t|| |d  ks@J t| |d d ks\J tdd	d
}t|d	k dkrt|d
kdksJ t|dk t|dk  krtjksn J t|t	dksJ t d}t
||}||dtjksJ ||ddksJ ||ddks"J t|}|ddkrF|d	dksJJ |tddtddkshJ |d
dkr|ddksJ d S )Nr  Tr   wr   r   r   r   r   r   r   r   r   g@r   r  r`  r   )r   rx   r   r@   r   r=   r   r   rD   r:   r?   r   rG   r
   )r  rt  r   r   r   r   r   r   r   test_uniform  s$    $, ru  c                  C   sT   t ddd} t ddd}td| | | }t|| k dkrLt|| | kdksPJ dS )	a   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.
    r  Tr   rt  r   r   r   N)r   rx   r=   )r  rt  r   r   r   r   test_uniform_P  s    rv  c                  C   s   t ddd} td}t d}td| }td| | | | d   t| | |dt|ft| d  }t|||s|J |j	j
jtd| ksJ t||t tt| d  | |  ksJ t||t|d | |  ksJ d S )	Nr  Tr  r   r   r   r   r   )r   r   ry   r   r   r   r   r?   r   rF   r   r   r4   rH   r	   r   rI   )r  r   r   r   r   r   r   r   test_uniformsum  s    
@.rw  c                  C   sZ   t d} t ddd}td| |}t|tt|tt|   dt td|  ksVJ d S )Nr   r   Tr   r   r   r   )r   rz   r?   r   r   r!   r   r$   )r   r   r   r   r   r   test_von_mises   s    rx  c                  C   s  t ddd\} }td| |}t| | tdd|   ks@J t| | d tdd|   t|d   ksxJ tt|dtdd|  d  dtdd|   tdd|    tdd|   tdd|  d  tdd|   tdd  ksJ tt	|dtdd|  d	  d
tdd|  d  tdd|    d	tdd|   tdd|    tdd	|   tdd|  d tdd|   d  ksJ d S )Nr   Tr   r   r   r   r   r  r   r  )
r   r{   r   r   r,   r@   r5   rB   r
   rC   r   r   r   r   test_weibull  s    $8 &"&ry  c               	   C   s   d} t jdtdddg}|D ]x}td| |}tt|t| tddt |   ksXJ tt|t| d tddt |   t|d  ksJ qd S )Nr   r   r   r   r   )	r   r   r
   r{   r5   r   r   r,   r@   )r   Zbvalsr   r   r   r   r   test_weibull_numeric  s    ,&rz  c                  C   s   t ddd} td| }t|jjt|  | ks2J t|tdttd  | d   t	| d   kshJ t
|dksxJ t|ttdtd| t  | t  ttdfdksJ d S )	NRTr   r   r   r   r   r   )r   r}   rF   r   r   r4   r?   r   r   r   r   rH   r   r%   r   )r{  r   r   r   r   test_wignersemicircle!  s    
6
(r|  c                     s   t d\} }t ddd\}t dddd\ttdd	  ttfd
d	 td|  ttfdd	 td ttttfD ]< tt fdd	 tt fdd	  d| qd S )Nr   zp qTr   zm nFr   c                   S   s   t dddS )Nr   r   r   rl   r   r   r   r   r   4  r   z-test_input_value_assertions.<locals>.<lambda>c                      s   t d S r   r}  r   )r  r  r   r   r   5  r   r   c                      s
   t d S r   )rX   r   )r  r   r   r   7  r   ZExc                      s    dS r   r   r   )fnr  r   r   r   r   :  r   c                      s    dS r   r   r   )r~  r  r   r   r   r   ;  r   r   )	r   r   r   rl   rX   rn   r{   rM   r]   )r   r   qr   )r~  r  r  r   r   test_input_value_assertions/  s    
r  c                  C   s,  t ddd} td}ttd| t|d  d  dtt  |t tf}ttdt|d  d  dtt  |dtf}ttp t	| dd
t|sJ t	| d dd
t|d sJ t| dkdd
t|sJ W d    n1 s0    Y  t| dk| d dk tjks(J d S )Nr   r   r   r   r   Fr%  )rl   r   r1   r   r   r   r   r   r)  r   r   r   r=   r   r   )r   r   expr1Zexpr2r   r   r   test_unevaluated?  s    82
$>r  c                  C   sT   t ddd} tt, tt| dkddtks2J W d    n1 sF0    Y  d S )NTrg  r   !   Fr%  )rl   r   r)  typer=   r   )r  r   r   r   test_probability_unevaluatedL  s    
r  c                  C   s:   t ddd} t ddd}tt| | ddtts6J d S )Nr   r   r   r   r   Fr%  )rl   rA  r?   r   r1   r   r   r   r   test_density_unevaluatedR  s    r  c            	      C   s  t dd} td}| |ttd| d d tj ks>J | d|dksRJ | ||dksfJ | |d |dks~J t|t dd}t	d}t
tdt|d d  d  dtt  |t df}|j|dk d	d
|du sJ t
tdt|d d  d  dtt  |dtf}|j|dkd	d
|du sFJ t|t dd}t
tdt|d d  d  dtt  |dtf}|j|dkd	d
|du sJ t
tdt|d d  d  dtt  |t df}|j|dk d	d
|du sJ d S )Nr   r   r   r   r   r$      r  Fr%  Tr#     r7  r  )r   r   rG   r(   r   r   r   Zexpectationr   r   r1   r   r   r   r*  r   )	Zndr   r   r$  r+  r,  r   Z	expected3Z	expected4r   r   r   test_NormalDistributionX  s"    
,8 6"6"8r  c                  C   s   t ddd} t d| d}t|ddts,J tt|ts>J t dddgdd	gd	dgg}tt|jtsnJ t|t t	d
t
td  d td
  tdd
   dt	t  ksJ d S )Nr   r   r   r  r   Fr%  r   r   r   rh  r   )rl   r?   r   rA  rF   r   rB  r   r5   r   r   r   r   )r   measr   r   r   r   test_random_parametersr  s    r  c                  C   s<   t ddd} t d| d}t|t| dt dddks8J d S )Nr   r   r   r  r   r   )rl   rE   r   )r   r  r   r   r   test_random_parameters_given|  s    r  c                  C   sB   t ddd} t d| d}ttt| t|tddtts>J d S )Nr   r   r   r   r   Fr%  )rl   rA  r5   r?   r   r   r   r   )r   r   r   r   r   test_conjugate_priors  s
    r  c                  C   sD   t ddd} t| d sJ tt| d s0J tt| s@J dS )z Since 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)rl   r?   r   r   r   r   r   r   test_difficult_univariate  s    r  c                  C   sF   t dd} tddd}t| dk tju s,J t|dk tju sBJ d S )Nr   r   gr   r   r   )rX   r]   r=   r   rj  )r   Gr   r   r   test_issue_10003  s    
r  c            	      C   s   t ddd} t ddd}t ddd\}}}t dddd}td	||td
||td|td|g}|D ]>}t|| t|jj	 |  }t|
t}|dksdJ qdd S )Nr   Tr   r   zsigma xm alphar   r  r
  r   r=   Cr   r   )r   rl   rn   rR   rX   rG   r5   rF   r?   Zcompute_cdfr   r)   )	r   r   r   r^  r   r  distribsr   Zcompdiffr   r   r   test_precomputed_cdf  s    

 r  c                     s   dd l   fdd} | tddddd | tddd j | tddd j | td	d
d j | tddd j  j | tddd j  j | tddddd | t	ddd j | t
ddddd | tdddd d S )Nr   c           
         s   t | }td}t|gt| |d}tt|g|tttt |  d  fdd}dD ]L}||}||}	tt|t|	 dk sJ tt	|t	|	 dk s`J q`d S )Nr   mpmathc                    s   j  fddgddS )Nc                    s
    | S r   r   r  )r   r   r   r   r     r   z^test_precomputed_characteristic_functions.<locals>.test_cf.<locals>.<lambda>.<locals>.<lambda>r   )Z	maxdegree)Zquadr   )r   r  support_lower_limitsupport_upper_limitr  r   r     r   zLtest_precomputed_characteristic_functions.<locals>.test_cf.<locals>.<lambda>)r   r   r     g-q=)
r?   r   r6   rH   r   r   r	   absr   r   )
distr  r  r   r   Zcf1Zcf2Z
test_pointZn1Zn2r  )r   r  r  r   test_cf  s    $z:test_precomputed_characteristic_functions.<locals>.test_cfr   r   r   r   r   r   r  r  r  r   r   rr   g      ?r   rt  r  )r  rM   rQ   infrR   rX   rd   rl   rq   rr   rx   r}   )r  r   r  r   )test_precomputed_characteristic_functions  s    r  c                  C   s4  t ddd} tdddtddd	d
tdddtddddtdddtdd
dtdddtdddt	dddt
dddtddg}|D ]B}tdD ]4}ttt|| | t|| | dddddsJ qqtdd}t|| t| d }t|d d!| t| d }tt|| || ddddds0J d S )"Nr   Tr   Ar   r#  Dr   r   r   r      r   Fr   r  r  r  r`  ZGIKr  ZLAr   iNr   r   r   )r   r   r   r   USFr%  )r   rK   rT   rV   r\   r]   r^   ra   rb   rd   rk   ru   rangetnr   rG   r?   ry   r   r   r   )r   r  Zdistr_r  Zpdf01Zcdf01r   r   r   test_long_precomputed_cdf  s(    







4
 r  c                  C   sF   t ddd} t| | tjktddks*J t| | dktjksBJ d S )Nr   r   r   r   r   )rx   r   r   r   r
   r   r   r   r   test_issue_13324  s    r  c                  C   sv   t ddd} t ddd}t| | tjks.J t| |d d  tjksLJ t|| | d  | |    tjksrJ d S )Nr   r   r   r   )rx   r   r   rj  r   r   r   r   test_issue_20756  s
    r  c                  C   sb   t dd} tddd}tt| dtju s.J tt|dtju sFJ tt|ttju s^J d S )Nr   r   r  r   r`  r   r   )rX   rl   r=   r   r   rj  r   )r   r  r   r   r   test_FiniteSet_prob  s
    
r  c                  C   s   t dd} tdd}tt| ddks*J tt|ddks@J tt|ddksVJ tt|ddkslJ tt| tdksJ d S )Nr   r   r   r   r   r   )rX   rR   r=   r   r   )r   r   r   r   r   test_prob_neq  s    

r  c                  C   s   t ddd} tt| d |  dkttd d ttdd d  tdd ksXJ tt| d d dktdtd d  d ttdd d  tdd ksJ d S )Nr  r   r   r   r   r   )rl   r5   r=   r(   r   r)   r
   r  r   r   r   
test_union  s    .6r  c                  C   s   t ddd} ttt| dk| dk ttd d ttdd d  tdd ksZJ tt| dk | dk t| dk ksJ tt| dk| dk dksJ d S )Nr  r   r   r   r   )rl   r5   r=   r3   r(   r   r)   r
   r  r   r   r   test_Or  s    .&r  c                  C   s   t dd} tt| dt| ddks(J tt| dt| ddksFJ t| dkt| ddksbJ t| dk t| ddks~J d S )Nr   r   r   r   )rX   r=   r   )r   r   r   r   test_conditional_eq  s
    
r  c               
   C   s"  t d} td}t| ttjd| k| dk @ fd| dk| dk @ ftj| dk| dk @ fd}t|tddd}t||}|j	t| ttdd | dk| dk @ fd| dk| dk @ ftdd | dk| dk @ fdksJ t
|jtddksJ t|jtddksJ t|jtd	d
ksJ d S )Nr   r   r   r   r   r   r   r      r   )r   r   r   r   r   r   r   r4   r   r   rD   valuer   r
   r@   )r   r   r   spacer   r   r   #test_ContinuousDistributionHandmade  s    ,
$.r  c                      s&   t ttdd tt fdd d S )Nr   r   c                      s   t  td tthS r   )r   r   r   r   r   r  r   r   r   +  r   z"test_issue_16318.<locals>.<lambda>)r   r   r4   r   r   r   r   r  r   test_issue_16318(  s    r  c                      s*   t ddtdd  tt fdd d S )Nr   r   r   r   c                      s   t  d   S )Nr   )r?   r   r   r   r   r   /  r   z&test_compute_density.<locals>.<lambda>)rl   r   r   r   r   r   r   r   test_compute_density-  s    r  N(  Zsympy.concrete.summationsr   Zsympy.core.functionr   r   r   Zsympy.core.mulr   Z
sympy.corer   r  r   r   r	   r
   r   Zsympy.core.relationalr   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r   r   Z(sympy.functions.combinatorial.factorialsr   r   Z$sympy.functions.elementary.complexesr   r   r   r   Z&sympy.functions.elementary.exponentialr   r   Z%sympy.functions.elementary.hyperbolicr   r   Z#sympy.functions.elementary.integersr   Z(sympy.functions.elementary.miscellaneousr   Z$sympy.functions.elementary.piecewiser   Z(sympy.functions.elementary.trigonometricr   r    r!   r"   r#   Zsympy.functions.special.besselr$   r%   r&   Z&sympy.functions.special.beta_functionsr'   Z'sympy.functions.special.error_functionsr(   r)   r*   r+   Z'sympy.functions.special.gamma_functionsr,   r-   r.   Z&sympy.functions.special.zeta_functionsr/   Zsympy.functions.special.hyperr0   Zsympy.integrals.integralsr1   Zsympy.logic.boolalgr2   r3   Zsympy.sets.setsr4   Zsympy.simplify.simplifyr5   Zsympy.utilities.lambdifyr6   r7   r9   r:   r;   r<   Zsympy.statsr=   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`   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   Zsympy.stats.crv_typesr   r   r   Zsympy.stats.joint_rv_typesr   r   Zsympy.stats.crvr   r   Zsympy.stats.compound_rvr   Z sympy.stats.symbolic_probabilityr   Zsympy.testing.pytestr   r   r   r   Zsympy.core.randomr   r  Infinityr   mapr   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.  r4  r5  r6  r8  r:  r>  r?  r@  rC  rF  rG  rH  rL  rM  rO  rS  rT  rY  r[  r]  r_  ra  rd  re  rf  rk  rl  rn  ro  rp  rs  ru  rv  rw  rx  ry  rz  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   <module>   s
   1  !

+	


	
	


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