ó
9­\c           @   s  d  d l  m Z m Z m Z m Z m Z m Z m Z m Z m	 Z	 m
 Z
 m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m  Z  m! Z! m" Z" m# Z# m$ Z$ 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/ m0 Z0 m1 Z1 m2 Z2 m3 Z3 m4 Z4 m5 Z5 m6 Z6 m7 Z7 m8 Z8 m9 Z9 m: Z: m; Z; m< Z< m= Z= m> Z> m? Z? m@ Z@ mA ZA mB ZB mC ZC mD ZD mE ZE mF ZF mG ZG mH ZH mI ZI mJ ZJ mK ZK mL ZL mM ZM mN ZN mO ZO mP ZP mQ ZQ mR ZR mS ZS mT ZT mU ZU mV ZV mW ZW mX ZX mY ZY mZ ZZ m[ Z[ m\ Z\ m] Z] m^ Z^ m_ Z_ m` Z` ma Za mb Zb mc Zc d  d ld me Ze d  d lf mg Zg d  d lh mi Zi mj Zj mk Zk ml Zl d  d lm mn Zo e jp Zq er e d	 ƒ \ Zs Zt Zu d
 „  Zv ej d „  ƒ Zw d „  Zx ek d „  ƒ Zy d „  Zz d „  Z{ d „  Z| d „  Z} d „  Z~ d „  Z d „  Z€ d „  Z d „  Z‚ d „  Zƒ d „  Z„ d „  Z… d „  Z† d „  Z‡ d „  Zˆ d „  Z‰ d „  ZŠ d „  Z‹ d  „  ZŒ d! „  Z d" „  ZŽ d# „  Z d$ „  Z d% „  Z‘ d& „  Z’ d' „  Z“ d( „  Z” d) „  Z• d* „  Z– d+ „  Z— d, „  Z˜ d- „  Z™ d. „  Zš d/ „  Z› d0 „  Zœ d1 „  Z d2 „  Zž ej d3 „  ƒ ZŸ d4 „  Z  d5 „  Z¡ d6 „  Z¢ ej d7 „  ƒ Z£ d8 „  Z¤ d9 „  Z¥ d: „  Z¦ d; „  Z§ d< „  Z¨ d= „  Z© ej d> „  ƒ Zª d? „  Z« d@ „  Z¬ dA „  Z­ dB „  Z® dC „  Z¯ dD „  Z° dE „  Z± dF „  Z² ek dG „  ƒ Z³ ek dH „  ƒ Z´ dI „  Zµ dJ „  Z¶ dK „  Z· dL „  Z¸ dM „  Z¹ dN „  Zº dO „  Z» dP S(Q   iÿÿÿÿ('   t   Symbolt   Abst   expt   St   Nt   pit   simplifyt   Intervalt   erft   erfct   Net   Eqt   logt
   lowergammat
   uppergammat   Sumt   symbolst   sqrtt   Andt   gammat   betat	   Piecewiset   Integralt   sint   cost   besselit	   factorialt   binomialt   floort   expand_funct   Rationalt   It   ret   imt   lambdifyt   hypert   difft   Ort   Mul(   t   range(   t   import_module(7   t   Pt   Et   wheret   densityt   variancet
   covariancet   skewnesst   givent   pspacet   cdft   characteristic_functiont   ContinuousRVt   samplet   Arcsint   Beninit   Betat	   BetaPrimet   Cauchyt   Chit
   ChiSquaredt   ChiNoncentralt   Dagumt   Erlangt   Exponentialt   FDistributiont   FisherZt   Frechett   Gammat   GammaInverset   Gompertzt   Gumbelt   Kumaraswamyt   Laplacet   Logistict	   LogNormalt   Maxwellt   Nakagamit   Normalt   Paretot
   QuadraticUt   RaisedCosinet   Rayleight   ShiftedGompertzt   StudentTt   Trapezoidalt
   Triangulart   Uniformt
   UniformSumt   VonMisest   Weibullt   WignerSemicirclet   correlationt   momentt   cmomentt   smoment(   t   NormalDistribution(   t   JointPSpace(   t   raisest   XFAILt   slowt   skip(   t   verify_numericallyt   xyzc          C   sZ  t  d d t d t ƒ}  t  d d t d t d t ƒ} t d d d ƒ } | | |  } t t | ƒ ƒ |  k st t ‚ t t | ƒ ƒ | d	 k s– t ‚ t | ƒ } t  d ƒ } | | ƒ d	 t j	 t
 |  | d	 d	 | d	 ƒ d	 t t j	 | k sÿ t ‚ t | d	 d k  ƒ t d	 t j	 d	 ƒ k s2t ‚ t | t | |  ƒ ƒ |  k sVt ‚ d  S(
   Nt   mut   realt   finitet   sigmat   positivet   xi    i   i   (   R    t   TrueRN   R   R*   t   AssertionErrorR-   R,   R   t   HalfR   R   R)   R   R   (   Rh   Rk   t   Xt   Yt   pdfRm   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_single_normal   s    "	H3c          C   s¿   t  d d d ƒ }  t |  |  d k ƒ } t | ƒ d t |  ƒ k sI t ‚ | j j j t d t ƒ k sm t ‚ t	 | ƒ t
 d ƒ t
 t ƒ k s• t ‚ t	 |  d ƒ t	 | d ƒ k s» t ‚ d  S(   NRm   i    i   i   (   RN   R0   R,   Ro   R1   t   domaint   setR   t   ooR*   R   R   (   Rq   Rr   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_conditional_1d/   s    "$(c             sð   t  d d d ƒ ‰  t ˆ  d d k ƒ j t d d ƒ k s@ t ‚ t ˆ  d d k ƒ j ˆ  j k sh t ‚ t t ˆ  d d k ˆ  d k ƒ ƒ j t d d ƒ k t t ‡  f d †  ƒ t	 ˆ  ˆ  d k ƒ }  |  j
 j j t d t ƒ k sì t ‚ d  S(   NRm   i    i   i   iÿÿÿÿc              s   t  t ˆ  ƒ d k ƒ S(   Ni   (   R+   R   (    (   Rq   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   <lambda>A   t    (   RN   R+   Rv   R   Ro   t   symbolR   Rb   t
   ValueErrorR0   R1   Ru   Rw   (   Rr   (    (   Rq   sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_ContinuousDomain<   s    .(5c          C   sR  t  d d d ƒ t  d d d ƒ }  } t |  | ƒ d k sA t ‚ t |  | ƒ d k s] t ‚ t |  |  ƒ d k sy t ‚ t |  | ƒ d k s” t ‚ t d |  | |  ƒ d t |  ƒ k sÂ t ‚ t |  ƒ d k sÚ t ‚ t |  | ƒ d k sö t ‚ t |  | ƒ d k st ‚ t |  |  | ƒ t |  |  | ƒ k s=t ‚ t |  d ƒ d k sXt ‚ t |  d ƒ d k sst ‚ t |  | d ƒ d	 k s’t ‚ t |  d ƒ t |  ƒ k s³t ‚ t	 |  |  d ƒ d k sÒt ‚ t	 |  | d ƒ t |  | ƒ k sût ‚ t |  t
 |  | d ƒ ƒ d k s#t ‚ t |  t
 |  | d ƒ ƒ t j k sNt ‚ d  S(
   NRm   i    i   t   yi   i   iþÿÿÿi   i   (   RN   R*   Ro   R-   R.   R/   R\   R]   R^   R_   R   R   Rp   (   Rq   Rr   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_multiple_normalH   s$    %.,!)(c          C   sö  t  d d t d t ƒ\ }  } t  d d t d t d t ƒ\ } } t d d t d t d t ƒ} t d |  | ƒ } t d | | ƒ } t d	 | ƒ } t  d
 d t d t ƒ\ } }	 }
 t | ƒ |  k sÌ t ‚ t | | ƒ |  | k sì t ‚ t | | |	 ƒ | t | ƒ |	 k st ‚ t | ƒ | d k s6t ‚ t t | | | |	 ƒ ƒ t | ƒ | d t | ƒ k sxt ‚ t | ƒ d | k s”t ‚ t | | |	 ƒ | t | ƒ |	 k sÂt ‚ t | | | |	 ƒ |  | | |	 k sòt ‚ d  S(   Ns   mu1 mu2Ri   Rj   s   sigma1 sigma2Rl   t   lambdaRm   R~   t   zs   a b ci   i   (	   R   Rn   R    RN   R@   R*   Ro   R-   R   (   t   mu1t   mu2t   s1t   s2t   rateRq   Rr   t   Zt   at   bt   c(    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_symbolic_   s    $! .B.c             sp  t  d d d ƒ ‰  t ˆ  ƒ }  t ˆ  d k  ƒ |  d ƒ j t ƒ k sK t ‚ |  d ƒ t j k sf t ‚ t ˆ  ˆ  d k ƒ }  |  d ƒ d k s“ t ‚ t d d ƒ ‰ t ˆ ƒ }  |  d ƒ d k sÆ t ‚ t ˆ d k ƒ d |  d ƒ k sî t ‚ t	 t
 ‡  ‡ f d †  ƒ t d	 d ƒ } t | ƒ } t d	 ƒ } | | ƒ t d t | ƒ | d k f d t f ƒ k slt ‚ d  S(
   NRm   i    i   R~   i
   iûÿÿÿi   c              s   t  ˆ  ˆ ƒ S(   N(   R2   (    (   Rq   Rr   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   ‚   Rz   R   (   RN   R2   R)   t   rewriteR	   Ro   R   Rp   R@   Rb   R|   R    R   R   Rn   (   t   dR‡   t   fR   (    (   Rq   Rr   sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_cdfs   s    -(c          C   s  t  d d d ƒ }  t |  ƒ } | d ƒ t d t t ƒ k sE t ‚ t d d d ƒ } t | ƒ } | d ƒ d k s{ t ‚ t | d ƒ ƒ t t t d ƒ d ƒ k s­ t ‚ t d d ƒ } t | ƒ } | d ƒ d k sà t ‚ t | d ƒ ƒ t d	 ƒ d
 d t d
 k st ‚ d  S(   NRm   i    i   iÿÿÿÿR~   i   R   i   i   i   (	   RW   R3   R   R   Ro   RN   R   R   R@   (   Rq   t   cfRr   R‡   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_characteristic_functionŠ   s    '2c          C   sÀ   t  d ƒ }  t |  t |  ƒ d t d t ƒ ƒ} t | ƒ | j j j k sR t	 ‚ t
 | j j ƒ  j ƒ  ƒ d \ } } | | k r˜ | t d t ƒ k sž t	 ‚ t | ƒ d ƒ d k s¼ t	 ‚ d  S(   NR   Rv   i    iÿÿÿÿ(   R    R4   R   R   Rw   R5   R1   Ru   Rv   Ro   t   listt   itemsR,   (   R   R‡   t   symt   val(    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_sample_continuous›   s    %!%'c          C   s¦   t  d ƒ }  t d ƒ t |  d d ƒ d t t ƒ } t |  | ƒ } t d d d ƒ } t | ƒ t | ƒ k sx t ‚ t | d k ƒ t | d k ƒ k s¢ t ‚ d  S(   NRm   i   R~   i    i   (	   R    R   R   R   R4   RN   R-   Ro   R)   (   Rm   Rs   Rq   Rr   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_ContinuousRV¤   s    -c       	   C   sí   d d l  m }  t d d t ƒ} t d d t ƒ} t d | | ƒ } t | ƒ t ƒ d t t t | t | ƒ k s t	 ‚ t
 | ƒ t ƒ t d | t k f d	 |  t | t | | ƒ ƒ t | t k f d t f ƒ k sé t	 ‚ d  S(
   Niÿÿÿÿ(   t   asinRˆ   Ri   R‰   Rm   i   i    i   (   t   sympyR˜   R    Rn   R6   R,   Rm   R   R   Ro   R2   R   (   R˜   Rˆ   R‰   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_arcsin¯   s    9!1c             s„  t  d d t ƒ‰  t  d d t ƒ‰ t  d d t ƒ‰ t d ˆ  ˆ ˆ ƒ }  t |  ƒ t ƒ ˆ  t d ˆ t t ˆ ƒ t t ˆ  t t ˆ ƒ ˆ t t ˆ ƒ d ƒ k s¶ t ‚ t  d d t ƒ‰  t	 t
 ‡  ‡ ‡ f d †  ƒ t  d d t ƒ‰ t	 t
 ‡  ‡ ‡ f d †  ƒ t  d d t ƒ‰  t	 t
 ‡  ‡ ‡ f d	 †  ƒ t  d d t ƒ‰ t  d d t ƒ‰ t	 t
 ‡  ‡ ‡ f d
 †  ƒ d  S(   Nt   alphaRl   R   Rk   Rm   i   c              s   t  d ˆ  ˆ ˆ ƒ S(   NRm   (   R7   (    (   R›   R   Rk   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   Æ   Rz   c              s   t  d ˆ  ˆ ˆ ƒ S(   NRm   (   R7   (    (   R›   R   Rk   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   É   Rz   c              s   t  d ˆ  ˆ ˆ ƒ S(   NRm   (   R7   (    (   R›   R   Rk   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   Ì   Rz   c              s   t  d ˆ  ˆ ˆ ƒ S(   NRm   (   R7   (    (   R›   R   Rk   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   Ð   Rz   (   R    Rn   R7   R,   Rm   R   R   Ro   t   FalseRb   R|   (   Rq   (    (   R›   R   Rk   sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_benini¼   s    0;c          C   sÈ  t  d d t ƒ\ }  } t d |  | ƒ } t | ƒ j j t d d ƒ k sQ t ‚ t | ƒ } t	 d ƒ } | | ƒ | |  d d | | d t
 |  | ƒ k s¦ t ‚ t t | ƒ ƒ |  |  | k sÌ t ‚ t t | ƒ ƒ |  | |  d d |  d | |  d d |  | d d |  | | d | d k s:t ‚ d \ }  } t d |  | ƒ } t t | ƒ ƒ |  t |  | ƒ k s„t ‚ t t | ƒ ƒ |  | t |  | d |  | d ƒ k sÄt ‚ d  S(	   Ns
   alpha betaRl   Rm   i    i   i   i   (   i   i   (   R   Rn   R8   R1   Ru   Rv   R   Ro   R,   R    R   R   R*   R-   R   R   (   Rˆ   R‰   t   Bt   densRm   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt	   test_betaÓ   s    '=&n,c             sæ   t  d d t ƒ‰  t  d d t ƒ‰ t d ˆ  ˆ ƒ }  t |  ƒ t ƒ t ˆ  d t d ˆ  ˆ t ˆ  ˆ ƒ k sz t ‚ t  d d t ƒ‰  t t	 ‡  ‡ f d †  ƒ t  d d t ƒ‰  t  d d t ƒ‰ t t	 ‡  ‡ f d †  ƒ d  S(   NR›   Rl   R   Rm   i   c              s   t  d ˆ  ˆ ƒ S(   NRm   (   R9   (    (   R›   t   betap(    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   ð   Rz   c              s   t  d ˆ  ˆ ƒ S(   NRm   (   R9   (    (   R›   R¡   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   ô   Rz   (
   R    Rn   R9   R,   Rm   R   Ro   Rœ   Rb   R|   (   Rq   (    (   R›   R¡   sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_betaprimeè   s    Dc             s   t  d ƒ ‰ t  d d t ƒ‰  t d ˆ ˆ  ƒ }  t |  ƒ t ƒ d t ˆ  d t ˆ d ˆ  d k sn t ‚ t  d d t ƒ‰  t t	 ‡  ‡ f d †  ƒ d  S(   Nt   x0R   Rl   Rm   i   i   c              s   t  d ˆ ˆ  ƒ S(   NRm   (   R:   (    (   R   R£   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   ÿ   Rz   (
   R    Rn   R:   R,   Rm   R   Ro   Rœ   Rb   R|   (   Rq   (    (   R   R£   sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_cauchy÷   s    >c             sÙ   t  d d t ƒ‰  t d ˆ  ƒ }  t |  ƒ t ƒ d ˆ  d d t ˆ  d t t d d ƒ t ˆ  d ƒ k sy t ‚ t  d d t d t ƒ‰  t	 t
 ‡  f d †  ƒ t  d d t d t ƒ‰  t	 t
 ‡  f d †  ƒ d  S(	   Nt   kt   integerRm   i   i   Rl   c              s   t  d ˆ  ƒ S(   NRm   (   R;   (    (   R¥   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   	  Rz   c              s   t  d ˆ  ƒ S(   NRm   (   R;   (    (   R¥   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy     Rz   (   R    Rn   R;   R,   Rm   R   R   Ro   Rœ   Rb   R|   (   Rq   (    (   R¥   sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_chi  s    Xc             sT  t  d d t ƒ‰  t  d ƒ ‰ t d ˆ  ˆ ƒ }  t |  ƒ t ƒ t ˆ  ˆ t ˆ ˆ  d t t d d ˆ d d ƒ t ˆ  d d t ˆ ƒ k sŸ t ‚ t  d d t d t ƒ‰  t	 t
 ‡  ‡ f d †  ƒ t  d d t d t ƒ‰  t  d d t ƒ‰ t	 t
 ‡  ‡ f d	 †  ƒ t  d d t ƒ‰  t  d d t ƒ‰ t	 t
 ‡  ‡ f d
 †  ƒ d  S(   NR¥   R¦   t   lRm   i   i   Rl   c              s   t  d ˆ  ˆ ƒ S(   NRm   (   R=   (    (   R¥   R¨   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy     Rz   c              s   t  d ˆ  ˆ ƒ S(   NRm   (   R=   (    (   R¥   R¨   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy     Rz   c              s   t  d ˆ  ˆ ƒ S(   NRm   (   R=   (    (   R¥   R¨   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy     Rz   (   R    Rn   R=   R,   Rm   R   R   Ro   Rœ   Rb   R|   (   Rq   (    (   R¥   R¨   sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_chi_noncentral  s    `c             sÏ  t  d d t ƒ‰  t d ˆ  ƒ }  t |  ƒ t ƒ d ˆ  d t ˆ  d d t t d ƒ t ˆ  d ƒ k su t ‚ t |  ƒ t ƒ t	 t
 ˆ  d t d ƒ t ˆ  d ƒ t d k f d t f ƒ k sÍ t ‚ t |  ƒ ˆ  k så t ‚ t |  ƒ d ˆ  k st ‚ t d d ƒ }  t |  ƒ d ƒ d	 t d
 ƒ t t d ƒ d ƒ d t t ƒ t t d
 ƒ d ƒ k sot ‚ t  d d t d t ƒ‰  t t ‡  f d †  ƒ t  d d t d t ƒ‰  t t ‡  f d †  ƒ d  S(   NR¥   R¦   Rm   i   i   i    i   i   içÅÿÿi   i  Rl   c              s   t  d ˆ  ƒ S(   NRm   (   R<   (    (   R¥   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   /  Rz   c              s   t  d ˆ  ƒ S(   NRm   (   R<   (    (   R¥   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   2  Rz   (   R    Rn   R<   R,   Rm   R   R   Ro   R2   R   R   R*   R-   R   R   R   R   Rœ   Rb   R|   (   Rq   (    (   R¥   sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_chi_squared"  s    TX_c             s—  t  d d t ƒ‰ t  d d t ƒ‰ t  d d t ƒ‰  t d ˆ ˆ  ˆ ƒ }  t |  ƒ t ƒ ˆ  ˆ t ˆ ˆ  ˆ t ˆ ˆ  d ˆ d t k sš t ‚ t |  ƒ t ƒ t d t ˆ ˆ  ˆ t d k f d t f ƒ k så t ‚ t  d d t ƒ‰ t	 t
 ‡  ‡ ‡ f d †  ƒ t  d d t ƒ‰ t  d d t ƒ‰ t	 t
 ‡  ‡ ‡ f d	 †  ƒ t  d d t ƒ‰ t  d d t ƒ‰  t	 t
 ‡  ‡ ‡ f d
 †  ƒ d  S(   Nt   pRl   R‰   Rˆ   Rm   i   i    c              s   t  d ˆ ˆ  ˆ ƒ S(   NRm   (   R>   (    (   Rˆ   R‰   R«   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   @  Rz   c              s   t  d ˆ ˆ  ˆ ƒ S(   NRm   (   R>   (    (   Rˆ   R‰   R«   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   D  Rz   c              s   t  d ˆ ˆ  ˆ ƒ S(   NRm   (   R>   (    (   Rˆ   R‰   R«   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   H  Rz   (   R    Rn   R>   R,   Rm   Ro   R2   R   Rœ   Rb   R|   (   Rq   (    (   Rˆ   R‰   R«   sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt
   test_dagum5  s    O3c          C   s×   t  d d t d t ƒ}  t  d d t ƒ} t d |  | ƒ } t | ƒ t ƒ t |  d | |  t t | ƒ t |  ƒ k sƒ t ‚ t | ƒ t ƒ t	 t
 |  | t ƒ t |  ƒ t d k f d t f ƒ k sÓ t ‚ d  S(   NR¥   R¦   Rl   R¨   Rm   i   i    (   R    Rn   R?   R,   Rm   R   R   Ro   R2   R   R   (   R¥   R¨   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_erlangK  s    G8c          C   sŒ  t  d d t d t d t ƒ}  t d |  ƒ } t | ƒ d |  k sI t ‚ t | ƒ d |  d k si t ‚ t | ƒ d k s t ‚ t | ƒ t | d ƒ k s¢ t ‚ t d | d	 ƒ t | d	 ƒ k sÊ t ‚ t | d ƒ d |  d k sí t ‚ t	 | d
 k ƒ t
 d ƒ k st ‚ t	 | d k ƒ t |  ƒ k s6t ‚ t	 | d k ƒ t d |  ƒ k s^t ‚ t | d k ƒ j t d
 d ƒ k sˆt ‚ d  S(   NR€   Rl   Ri   Rj   Rm   i   i   i   i   i    i
   iöÿÿÿi   i   (   R    Rn   R@   R*   Ro   R-   R/   R_   R]   R)   R   R   R+   Rv   R   (   R†   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_exponentialU  s     !(#$%(c          C   s    t  d d t ƒ}  t  d d t ƒ} t d |  | ƒ } t | ƒ t ƒ | | d t |  t |  |  t | |  | ƒ t t |  d | d ƒ k sœ t ‚ d  S(   Nt   d1Rl   t   d2Rm   i   (   R    Rn   RA   R,   Rm   R   R   Ro   (   R¯   R°   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_f_distributionf  s
    c          C   sº   t  d d t ƒ}  t  d d t ƒ} t d |  | ƒ } t | ƒ t ƒ d |  |  d | | d |  t d t ƒ | |  d | d t |  t ƒ t |  d | d ƒ k s¶ t ‚ d  S(   NR¯   Rl   R°   Rm   i   (   R    Rn   RB   R,   Rm   R   R   Ro   (   R¯   R°   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_fisher_zn  s
    c          C   sò   t  d d t ƒ}  t  d d t ƒ} t  d d t ƒ} t d |  d | d | ƒ} t | ƒ t ƒ |  t | | |  d t t | | |  ƒ | k s  t ‚ t | ƒ t ƒ t t | t | |  ƒ | t k f d t f ƒ k sî t ‚ d  S(	   NRˆ   Rl   t   st   mRi   Rm   i   i    (	   R    Rn   RC   R,   Rm   R   Ro   R2   R   (   Rˆ   R³   R´   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_frechetv  s    Oc          C   s»  t  d d t ƒ}  t  d d t ƒ} t d |  | ƒ } t | ƒ t ƒ t |  d | |  t t | ƒ t |  ƒ k s~ t ‚ t | d t ƒt	 ƒ t
 |  t |  d ƒ t |  d ƒ |  t |  t	 | ƒ t |  d ƒ t	 d k f d t f ƒ k sü t ‚ t | ƒ t | d ƒ k st ‚ t d d	 t d
 t d t ƒ\ }  } t d |  | ƒ } t | ƒ |  | k sot ‚ t | ƒ |  | d k st ‚ t t | ƒ ƒ d t |  ƒ k s·t ‚ d  S(   NR¥   Rl   t   thetaRm   i   t   meijergi    s   k thetaRi   Rj   i   (   R    Rn   RD   R,   Rm   R   R   Ro   R2   R   R   R   R*   R]   R   R-   R   R/   R   (   R¥   R¶   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt
   test_gamma€  s    H/!$ c          C   sÒ   t  d d t ƒ}  t  d d t ƒ} t d |  | ƒ } t | ƒ t ƒ t |  d | |  t | t ƒ t |  ƒ k s~ t ‚ t | ƒ t ƒ t	 t
 |  | t ƒ t |  ƒ t d k f d t f ƒ k sÎ t ‚ d  S(   NRˆ   Rl   R‰   Rm   i   i    (   R    Rn   RE   R,   Rm   R   R   Ro   R2   R   R   (   Rˆ   R‰   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_gamma_inverse”  s
    Hc          C   sV   t  d ƒ }  |  s t d ƒ n  t d d d ƒ } t | ƒ | j j j k sR t ‚ d  S(   Nt   scipys?   Scipy not installed. Abort tests for sampling of gamma inverse.Rm   i   (   R(   Re   RE   R5   R1   Ru   Rv   Ro   (   Rº   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_sampling_gamma_inverseœ  s
    c          C   s   t  d d t ƒ}  t  d d t ƒ} t d |  | ƒ } t | ƒ t ƒ |  | t | ƒ t |  t ƒ t | t |  t ƒ ƒ k s‰ t ‚ d  S(   NR‰   Rl   t   etaRm   (   R    Rn   RF   R,   Rm   R   Ro   (   R‰   R¼   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_gompertz£  s    c          C   s—   t  d d t ƒ}  t  d ƒ } t  d ƒ } t d |  | ƒ } t t | ƒ | ƒ ƒ d k s` t ‚ t | ƒ | ƒ t t | | |  ƒ ƒ k s“ t ‚ d  S(   NR   Rl   Rh   Rm   s0   exp(-exp(-(-mu + x)/beta) - (-mu + x)/beta)/beta(   R    Rn   RG   t   strR,   Ro   R2   R   (   R   Rh   Rm   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_gumbel«  s    $c          C   s×   t  d d t ƒ}  t  d d t ƒ} t d |  | ƒ } t | ƒ t ƒ t |  d |  | t |  d | d k sy t ‚ t | ƒ t ƒ t d t d k  f t |  d | d t d k f d t f ƒ k sÓ t ‚ d  S(   NRˆ   Rl   R‰   Rm   i   i    (   R    Rn   RH   R,   Rm   Ro   R2   R   (   Rˆ   R‰   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_kumaraswamy´  s    C!!c          C   sÒ   t  d ƒ }  t  d d t ƒ} t d |  | ƒ } t | ƒ t ƒ t t t |  ƒ | ƒ d | k sk t ‚ t | ƒ t ƒ t	 t |  t | ƒ d |  t k f t |  t | ƒ d d t f ƒ k sÎ t ‚ d  S(   NRh   R‰   Rl   Rm   i   i   (
   R    Rn   RI   R,   Rm   R   R   Ro   R2   R   (   Rh   R‰   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_laplace¿  s    ;4c          C   sº   t  d d t ƒ}  t  d d t ƒ} t d |  | ƒ } t | ƒ t ƒ t t |  | ƒ | t t |  | ƒ d d k s‚ t ‚ t | ƒ t ƒ d t |  t | ƒ d k s¶ t ‚ d  S(   NRh   Ri   R³   Rl   Rm   i   i   (   R    Rn   RJ   R,   Rm   R   Ro   R2   (   Rh   R³   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_logisticÈ  s
    Lc          C   s–  t  d d t d t ƒ}  t  d d t d t d t ƒ} t d |  | ƒ } xP t d ƒ D]B } t d | d ƒ } t t | ƒ ƒ t t | ƒ ƒ k sU t ‚ qU Wt  d d t ƒ} t  d d t ƒ} t d | | ƒ } t	 | ƒ t
 ƒ t d	 ƒ t | t t
 ƒ d	 d	 | d	 ƒ d	 t
 t t ƒ | k s1t ‚ t d d d
 ƒ } t	 | ƒ t
 ƒ t d	 ƒ t t t
 ƒ d	 d	 ƒ d	 t
 t t ƒ k s’t ‚ d  S(   NRh   Ri   Rj   Rk   Rl   Rm   i   i    i   i   (   R    Rn   RK   R'   R   R5   R   R   Ro   R,   Rm   R   R   R   (   t   meant   stdRq   t   iRh   Rk   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_lognormalÑ  s    .Qc          C   sà   t  d d t ƒ}  t d |  ƒ } t | ƒ t ƒ t d ƒ t d t t d d |  d ƒ t t ƒ |  d k sz t ‚ t	 | ƒ d t d ƒ |  t t ƒ k sª t ‚ t
 t | ƒ ƒ |  d d d t t k sÜ t ‚ d  S(   NRˆ   Rl   Rm   i   i   iøÿÿÿ(   R    Rn   RL   R,   Rm   R   R   R   Ro   R*   R   R-   (   Rˆ   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_maxwellì  s    ;0c          C   s•  t  d d t ƒ}  t  d d t ƒ} t d |  | ƒ } t | ƒ t ƒ d t d |  d |  |  | |  t t d |  | ƒ t |  ƒ k s– t ‚ t t	 | ƒ ƒ t
 |  ƒ t
 | ƒ t |  t j ƒ t |  d ƒ k sã t ‚ t t | ƒ ƒ | | t |  t d ƒ d ƒ d t |  ƒ t |  d ƒ k s9t ‚ t | ƒ t ƒ t t |  |  t d | ƒ t |  ƒ t d k f d t f ƒ k s‘t ‚ d  S(   NRh   Rl   t   omegaRm   i   i   i    (   R    Rn   RM   R,   Rm   R   R   Ro   R   R*   R   R   Rp   R-   R2   R   R   (   Rh   RÈ   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_nakagami÷  s    Q>G.c          C   s­   t  d d t d t ƒ\ }  } | d } t d |  | ƒ } t | ƒ } t d ƒ } | | ƒ | | d |  | | k s t ‚ t t | ƒ ƒ | |  | d k s© t ‚ d  S(   Ns   xm betaRl   Rj   i   Rm   i   (   R   Rn   RO   R,   R    Ro   R   R*   (   t   xmR   R›   Rq   RŸ   Rm   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_pareto  s    
-c          C   s   d \ }  } | d } t  d |  | ƒ } t | ƒ | |  t | d ƒ k sR t ‚ t | ƒ |  d | t | d d | d ƒ k sŒ t ‚ d  S(   Ni   i   i   Rm   i   (   i   i   (   RO   R*   R   Ro   R-   (   RÊ   R   R›   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_pareto_numeric  s
    
*c          C   s¨   t  d d t ƒ}  t  d d t ƒ} t d |  | ƒ } t | ƒ t ƒ t t t t |  | ƒ d d | t t |  | k |  | t k ƒ f d t f ƒ k s¤ t	 ‚ d  S(	   NRh   Ri   R³   Rl   Rm   i   i   i    (
   R    Rn   RQ   R,   Rm   R   R   R   R   Ro   (   Rh   R³   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_raised_cosine   s
    3c          C   sÇ   t  d d t ƒ}  t d |  ƒ } t | ƒ t ƒ t t t d d |  d ƒ |  d k sb t ‚ t | ƒ t d ƒ t t	 ƒ |  d k s’ t ‚ t
 | ƒ t	 |  d d d |  d k sÃ t ‚ d  S(   NRk   Rl   Rm   i   (   R    Rn   RR   R,   Rm   R   Ro   R*   R   R   R-   (   Rk   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_rayleigh)  s
    A0c          C   sœ   t  d d t ƒ}  t  d d t ƒ} t d |  | ƒ } t | ƒ t ƒ |  | d t |  t ƒ d t |  t ƒ t | t |  t ƒ ƒ k s˜ t ‚ d  S(   NR‰   Rl   R¼   Rm   i   (   R    Rn   RS   R,   Rm   R   Ro   (   R‰   R¼   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_shiftedgompertz2  s    c          C   s=  t  d d t ƒ}  t d |  ƒ } t | ƒ t ƒ d t d |  |  d t d ƒ d t |  ƒ t t d ƒ d |  d ƒ k s‡ t ‚ t	 | ƒ t ƒ t d ƒ d t t
 |  d t d ƒ d ƒ t t d ƒ d |  d t d ƒ d f t d ƒ d f t d |  ƒ t t ƒ t |  ƒ t
 |  d ƒ k s9t ‚ d  S(   Nt   nuRl   Rm   i   i   i   (   R    Rn   RT   R,   Rm   R   R   R   Ro   R2   R   R#   R   (   RÐ   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_studentt9  s
    fc          C   sº  t  d d t ƒ}  t  d d t ƒ} t  d d t ƒ} t  d d t ƒ} t d |  | | | ƒ } t | ƒ t ƒ t d |  d t |  | |  | | | |  t k t | k  @f d |  | | | | t k t | k  @f d | d t | | |  | | | | t k t | k @f d	 t f ƒ k s2t ‚ t d d	 d
 d d ƒ } t | ƒ t d ƒ d k slt ‚ t	 | ƒ t d ƒ d k sŽt ‚ t
 | d k  ƒ t d ƒ d k s¶t ‚ d  S(   NRˆ   Ri   R‰   RŠ   R   Rm   iþÿÿÿi   i    i   i   i   i   i   (   R    Rn   RU   R,   Rm   R   Ro   R*   R   R-   R)   (   Rˆ   R‰   RŠ   R   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_trapezoidalB  s    Q*?""c       	   C   sö   t  d ƒ }  t  d ƒ } t  d ƒ } t d |  | | ƒ } t | ƒ t ƒ t d t d |  |  | |  | t |  t k t | k  ƒ f d |  | t | k f d t d | |  | | | t t | k | t k  ƒ f d t f ƒ k sò t ‚ d  S(   NRˆ   R‰   RŠ   Rm   i   iþÿÿÿi    (   R    RV   R,   Rm   R   R   Rn   Ro   (   Rˆ   R‰   RŠ   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_triangularS  s    <;c          C   s§   t  d d t ƒ}  t  d d t ƒ} t d |  | ƒ } t | ƒ t ƒ t d t |  d | d d |  | d t t | k |  t k ƒ f d t f ƒ k s£ t ‚ d  S(	   NRˆ   Ri   R‰   Rm   i   i   i   i    (   R    Rn   RP   R,   Rm   R   R   Ro   (   Rˆ   R‰   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_quadratic_ua  s
    :c          C   s)  t  d d t d t ƒ}  t  d d t d t ƒ} t d |  |  | ƒ } t t | ƒ ƒ |  | d k sl t ‚ t t | ƒ ƒ | d d k s’ t ‚ t d d	 d
 ƒ } t | d	 k  ƒ d k rÔ t | d
 k ƒ d k sÚ t ‚ t | d k  ƒ t | d k ƒ k ot j	 k n st ‚ t  d ƒ } t
 | ƒ | ƒ } | j | d ƒ t d ƒ d k s]t ‚ | j | d ƒ d k s{t ‚ | j | d ƒ d k s™t ‚ t | ƒ } | d ƒ d k rÉ| d	 ƒ d k sÏt ‚ | t d ƒ d ƒ t d ƒ d k sût ‚ | d
 ƒ d k r| d ƒ d k s%t ‚ d  S(   NR¨   Ri   Rj   t   wRl   Rm   i   i   i   i   i    i   R   gš™™™™™@i   iÿÿÿÿi   i   (   R    Rn   RW   R   R*   Ro   R-   R)   R   Rp   R,   t   subsR2   (   R¨   RÕ   Rq   R   R«   RŠ   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_uniformj  s"    &&6=(*,c          C   s„   t  d d t d t ƒ}  t  d d t d t ƒ} t d |  |  | ƒ } t | |  k  ƒ d k rz t | |  | k ƒ d k s€ t ‚ d S(	   sŽ   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¨   Ri   Rj   RÕ   Rl   Rm   i    N(   R    Rn   RW   R)   Ro   (   R¨   RÕ   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_uniform_Pƒ  s    	c          C   s—   t  d d t ƒ}  t  d ƒ } t d |  ƒ } t | ƒ t ƒ t d | | t |  d t |  | ƒ | d t t ƒ f ƒ t |  d ƒ k s“ t	 ‚ d  S(   Nt   nR¦   R¥   Rm   iÿÿÿÿi   i    (
   R    Rn   RX   R,   Rm   R   R   R   R   Ro   (   RÙ   t   _kRq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_uniformsum’  s
    c          C   s{   t  d ƒ }  t  d d t ƒ} t d |  | ƒ } t | ƒ t ƒ t | t t |  ƒ ƒ d t t d | ƒ k sw t	 ‚ d  S(   NRh   R¥   Rl   Rm   i   i    (
   R    Rn   RY   R,   Rm   R   R   R   R   Ro   (   Rh   R¥   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_von_misesœ  s    c          C   sQ  t  d d t ƒ\ }  } t d |  | ƒ } t t | ƒ ƒ t |  t d d | ƒ ƒ k s` t ‚ t t | ƒ ƒ t |  d t d d | ƒ t | ƒ d ƒ k s¨ t ‚ t t | ƒ ƒ d t d d | ƒ d d t d d | ƒ t d d | ƒ t d d | ƒ t d d | ƒ d t d d | ƒ t	 d ƒ d k sMt ‚ d  S(   Ns   a bRl   Rm   i   i   i   (
   R   Rn   RZ   R   R*   R   Ro   R-   R/   R   (   Rˆ   R‰   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_weibull¤  s
    6Hc       	   C   sÖ   d }  t  j d t  d ƒ d d g } xª | D]¢ } t d |  | ƒ } t t | ƒ ƒ t |  t d d t  | ƒ ƒ ƒ k s€ t ‚ t t | ƒ ƒ t |  d t d d t  | ƒ ƒ t | ƒ d ƒ k s, t ‚ q, Wd  S(   Ni   i   i   i   Rm   (	   R   Rp   RZ   R   R*   R   R   Ro   R-   (   Rˆ   t   bvalsR‰   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_weibull_numeric¬  s    <c          C   s~   t  d d t ƒ}  t d |  ƒ } t | ƒ t ƒ d t t d |  d ƒ t |  d k sb t ‚ t | ƒ d k sz t ‚ d  S(   Nt   RRl   Rm   i   i    (	   R    Rn   R[   R,   Rm   R   R   Ro   R*   (   Rà   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_wignersemicircle¸  s    Ac          C   sþ   t  d d d ƒ }  t d d d ƒ } t d d ƒ } t d d d ƒ } t d d d ƒ } t d	 d d ƒ } t d
 d d ƒ } t d d d ƒ } |  | | | | | | | g } d }	 xF | D]> }
 x5 t |	 ƒ D]' } t	 |
 ƒ |
 j
 j j k sË t ‚ qË Wq¸ Wd  S(   NRq   i    i   t   Lt   ExR)   i   t   Wt   URž   i   i   t   Gi
   (   RN   RK   R@   RO   RZ   RW   R8   RD   R'   R5   R1   Ru   Rv   Ro   (   R   Râ   R*   R)   Rä   Rå   Rž   Ræ   t	   variablest   nitert   varRÅ   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_prefab_samplingÀ  s    c             s  t  d ƒ \ }  } t  d d t ƒ\ ‰ } t  d d t d t ƒ\ ‰ ‰ t t d „  ƒ t t ‡ ‡ f d †  ƒ t d |  ˆ ƒ t t ‡ f d	 †  ƒ t d
 ˆ ƒ xb t t t	 t
 g D]N ‰  t t ‡  ‡ ‡ f d †  ƒ t t ‡  ‡ ‡ f d †  ƒ ˆ  d ˆ | ƒ q· Wd  S(   Ns   a bs   p qRl   s   m nRi   c           S   s   t  d d d ƒ S(   NRm   i   i    (   RN   (    (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   Ö  Rz   c              s   t  d ˆ  ˆ ƒ S(   NRm   (   RN   (    (   R´   RÙ   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   ×  Rz   Rq   c              s   t  d ˆ  ƒ S(   NRm   (   R@   (    (   R´   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   Ù  Rz   Rã   c              s   ˆ  d ˆ ˆ ƒ S(   NRm   (    (    (   t   fnR´   R«   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   Ü  Rz   c              s   ˆ  d ˆ ˆ ƒ S(   NRm   (    (    (   Rë   RÙ   R«   (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   Ý  Rz   Rm   (   R   Rn   Rœ   Rb   R|   RN   R@   RO   RZ   R8   RD   (   Rˆ   R‰   t   q(    (   Rë   R´   RÙ   R«   sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_input_value_assertionsÑ  s    c       	   C   sÚ  t  d d d ƒ }  t |  d t ƒt t d ƒ t t t d d ƒ d t t ƒ t t t f ƒ k sn t	 ‚ t |  d d t ƒt t d ƒ t t t d d ƒ d t t ƒ t t t f ƒ d k sÒ t	 ‚ t
 |  d k d t ƒt t d ƒ t t d d ƒ d t t ƒ t d t f ƒ k s/t	 ‚ t
 |  d k |  d d k  d t ƒt t d ƒ t t d d ƒ d t t ƒ t t d ƒ t t d d ƒ d t t ƒ t d d f ƒ t d d f ƒ k sÖt	 ‚ d  S(   NRm   i    i   t   evaluatei   iÿÿÿÿ(   RN   R*   Rœ   R   R   Rm   R   R   Rw   Ro   R)   (   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_unevaluatedá  s    MQH",-c          C   s@   t  d d d ƒ }  t t |  d k d t ƒƒ t k s< t ‚ d  S(   Nt   Ti   i   i!   Rî   (   RN   t   typeR)   Rœ   R   Ro   (   Rð   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_probability_unevaluatedó  s    c          C   sS   t  d d d ƒ }  t  d d d ƒ } t t |  | d t ƒt ƒ t ƒ sO t ‚ d  S(   NRq   i    i   Rr   i   Rî   (   RN   t
   isinstanceR,   Rœ   R   R   Ro   (   Rq   Rr   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_density_unevaluatedø  s    c          C   så   t  d d ƒ }  t d ƒ } |  j | ƒ t t d ƒ | d ƒ d t j d k sY t ‚ t |  j	 ƒ  t
 ƒ sƒ |  j	 ƒ  j sƒ t ‚ |  j d | ƒ d k s¡ t ‚ |  j | | ƒ d k s¿ t ‚ |  j | d | ƒ d k sá t ‚ d  S(   Ni    i   Rm   i   (   R`   R    R2   R   R   R   t   OneRo   Ró   R5   t   floatt	   is_Numbert   expectation(   t   ndRm   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_NormalDistributionþ  s    >*c          C   sa   t  d d d ƒ }  t  d |  d ƒ } t | d t ƒt ƒ sB t ‚ t t | ƒ t ƒ s] t ‚ d  S(   NRh   i   i   Rð   i   Rî   (   RN   R,   Rœ   R   Ro   Ró   R1   Ra   (   Rh   t   meas(    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_random_parameters  s    c          C   sX   t  d d d ƒ }  t  d |  d ƒ } t | t |  d ƒ ƒ t  d d d ƒ k sT t ‚ d  S(   NRh   i   i   Rð   i   i   (   RN   R0   R   Ro   (   Rh   Rû   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_random_parameters_given  s    c          C   sa   t  d d d ƒ }  t  d |  d ƒ } t t t |  t | t ƒ d t ƒt ƒ ƒ t ƒ s] t	 ‚ d  S(   NRh   i   i   Rm   i   Rî   (
   RN   Ró   R   R,   R   R~   Rœ   R   R&   Ro   (   Rh   Rm   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_conjugate_priors  s    *c          C   s`   t  d d d ƒ }  t |  d ƒ s( t ‚ t t |  d ƒ ƒ sD t ‚ t t |  ƒ ƒ s\ t ‚ d S(   s¢    Since using solve in place of deltaintegrate we're able to perform
    substantially more complex density computations on single continuous random
    variables Rm   i    i   i   i   N(   RN   R,   Ro   R   R   (   Rm   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_difficult_univariate  s    c          C   sg   t  d d ƒ }  t d d d ƒ } t |  d k  ƒ t j k sB t ‚ t | d k  ƒ t j k sc t ‚ d  S(   NRm   i   t   gi   i   iÿÿÿÿ(   R@   RD   R)   R   t   ZeroRo   (   Rq   Ræ   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_issue_10003(  s    !c    	      C   s  t  d d t d t ƒ}  t  d d t d t ƒ} t  d d t d t ƒ\ } } } t  d d t d t d t ƒ} t d	 | | ƒ t d
 | | ƒ t d | ƒ t d | ƒ g } xc | D][ } t | ƒ |  ƒ t | j j	 j
 ƒ  |  ƒ ƒ } t | j t ƒ ƒ } | d k s² t ‚ q² Wd  S(   NRm   Ri   Rj   Rh   s   sigma xm alphaRl   RÙ   R¦   Rq   R)   t   CR*   i    (   R   Rn   RN   RO   R<   R@   R2   R   R1   R,   t   compute_cdfRŒ   R	   Ro   (	   Rm   Rh   Rk   RÊ   R›   RÙ   t   distribsRq   t   compdiff(    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_precomputed_cdf/  s    !.c             sB  d d  l  ‰  ‡  f d †  }  |  t d d d ƒ d d ƒ |  t d d ƒ d ˆ  j ƒ |  t d d ƒ d ˆ  j ƒ |  t d	 d
 ƒ d ˆ  j ƒ |  t d d d ƒ ˆ  j ˆ  j ƒ |  t d d d ƒ ˆ  j ˆ  j ƒ |  t d d d ƒ d d ƒ |  t	 d d ƒ d ˆ  j ƒ |  t
 d d d ƒ d d ƒ |  t d d ƒ d d ƒ d  S(   Niÿÿÿÿc            s  t  |  ƒ } t d ƒ } t d ƒ } t | g t |  ƒ | ƒ d ƒ } t | | g | | ƒ t t | | ƒ d ƒ ‰  ‡  ‡ ‡ ‡ f d †  } x‚ d d d d g D]n } | | ƒ }	 | | ƒ }
 t t |	 ƒ t |
 ƒ ƒ d	 k  sæ t ‚ t t	 |	 ƒ t	 |
 ƒ ƒ d	 k  s  t ‚ q  Wd  S(
   Nt   tRm   t   mpmathc            s(   ˆ j  ‡ ‡  f d †  ˆ ˆ g d d ƒS(   Nc            s   ˆ  |  ˆ ƒ S(   N(    (   Rm   (   RŽ   R  (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   P  Rz   t	   maxdegreei
   (   t   quad(   R  (   RŽ   R	  t   support_lower_limitt   support_upper_limit(   R  sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyRy   P  Rz   i   i   i   i   gê-™—q=(
   R,   R    R"   R3   R   R   t   absR    Ro   R!   (   t   distR  R  Rs   R  Rm   t   cf1t   cf2t
   test_pointt   n1t   n2(   R	  (   RŽ   R  R  sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_cfF  s    !0(R‰   i   i   i    RŠ   i   t   ei   R¨   RÙ   i   t   ri   g      à?t   uRÕ   iýÿÿÿ(   R	  R8   R;   t   infR<   R@   RJ   RN   RQ   RR   RW   R[   (   R  (    (   R	  sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt)   test_precomputed_characteristic_functionsB  s    ##c          C   så  t  d d t d t ƒ}  t d d d ƒ t d d d	 d
 ƒ t d d d ƒ t d d d d ƒ t d d d ƒ t d d
 d ƒ t d d d ƒ t	 d d d ƒ t
 d d d ƒ t d d d ƒ t d d ƒ g } xv | D]n } xe t d ƒ D]W } t t t | ƒ |  ƒ |  ƒ t | ƒ |  ƒ |  d d d d d d  d! d ƒsà t ‚ qà WqÍ Wt d" d ƒ } t | ƒ |  ƒ j t |  ƒ d ƒ j ƒ  } t | d# t ƒ|  ƒ j t |  ƒ d ƒ j ƒ  } t t | |  ƒ | |  d d d d d d  d! d ƒsát ‚ d  S($   NRm   Ri   Rj   t   Aiûÿÿÿi	   t   Di   i
   i   R*   i   i   t   Fi   i   iýÿÿÿRæ   i   t   GIt   Ki   t   LARâ   iúÿÿÿR   R   Rˆ   i    R‰   RŠ   i   R   t   USRî   (   R   Rn   R6   R>   R?   RC   RD   RE   RH   RI   RJ   RM   RT   R'   t   tnR$   R2   R,   Ro   RX   RÖ   R   t   doitRœ   (   Rm   R  t   distrt   _R!  t   pdf01t   cdf01(    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_long_precomputed_cdff  s&    Y*0c          C   ss   t  d d d ƒ }  t |  |  t d d ƒ k ƒ t d d ƒ k sE t ‚ t |  |  d k ƒ t d d ƒ k so t ‚ d  S(   NRq   i    i   i   i   i   (   RW   R*   R   Ro   (   Rq   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_issue_13324  s    3c          C   s   t  d ƒ }  t d d ƒ } t d d d ƒ } t t | d ƒ ƒ t j k sQ t ‚ t t | d ƒ ƒ t j k su t ‚ t t | |  ƒ ƒ t j k s™ t ‚ d  S(	   NRm   R*   i   R   i   i   i   i   (   R   R@   RN   R)   R   R   R  Ro   (   Rm   R*   R   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_FiniteSet_prob„  s    $$c          C   sÓ   t  d d ƒ }  t d d ƒ } t d ƒ } t t |  d ƒ ƒ d k sK t ‚ t t | d ƒ ƒ d k sl t ‚ t t | d ƒ ƒ d k s t ‚ t t | d ƒ ƒ d k s® t ‚ t t |  | ƒ ƒ d k sÏ t ‚ d  S(   NR*   i   Rq   Rm   i   i   i   (   R@   R<   R   R)   R
   Ro   (   R*   Rq   Rm   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_prob_neqŒ  s    !!!!c          C   sä   t  d d d ƒ }  t t |  d |  d k ƒ ƒ t t d ƒ ƒ d t t d ƒ d ƒ d t d ƒ d k su t ‚ t t |  d d d k ƒ ƒ t d t d ƒ d ƒ d t t d ƒ d ƒ d t d ƒ d k sà t ‚ d  S(   NR   i   i   i   i    i   (   RN   R   R)   R   R   R	   R   Ro   (   R   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt
   test_union–  s
    Fc          C   sæ   t  d d d ƒ }  t t t |  d k |  d k  ƒ ƒ ƒ t t d ƒ ƒ d t t d ƒ d ƒ d t d ƒ d k s| t ‚ t t |  d k  |  d k  ƒ ƒ t |  d k  ƒ k sµ t ‚ t t |  d k |  d k  ƒ ƒ d k sâ t ‚ d  S(   NR   i    i   i   i   (	   RN   R   R)   R%   R   R   R	   R   Ro   (   R   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_Or  s
    $F9c          C   sÁ   t  d d ƒ }  t t |  d ƒ t |  d ƒ ƒ d k s< t ‚ t t |  d ƒ t |  d ƒ ƒ d k si t ‚ t |  d k t |  d ƒ ƒ d k s“ t ‚ t |  d k  t |  d ƒ ƒ d k s½ t ‚ d  S(   NR*   i   i   i    (   R@   R)   R   Ro   (   R*   (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   test_conditional_eq¥  s
    --*N(¼   R™   R    R   R   R   R   R   R   R   R   R	   R
   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R    R!   R"   R#   R$   R%   R&   t   sympy.core.compatibilityR'   t   sympy.externalR(   t   sympy.statsR)   R*   R+   R,   R-   R.   R/   R0   R1   R2   R3   R4   R5   R6   R7   R8   R9   R:   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_   t   sympy.stats.crv_typesR`   t   sympy.stats.joint_rvRa   t   sympy.utilities.pytestRb   Rc   Rd   Re   t   sympy.utilities.randtestRf   R"  t   InfinityRw   t   mapRm   R~   R   Rt   Rx   R}   R   R‹   R   R‘   R–   R—   Rš   R   R    R¢   R¤   R§   R©   Rª   R¬   R­   R®   R±   R²   Rµ   R¸   R¹   R»   R½   R¿   RÀ   RÁ   RÂ   RÆ   RÇ   RÉ   RË   RÌ   RÍ   RÎ   RÏ   RÑ   RÒ   RÓ   RÔ   R×   RØ   RÛ   RÜ   RÝ   Rß   Rá   Rê   Rí   Rï   Rò   Rô   Rú   Rü   Rý   Rþ   Rÿ   R  R  R  R(  R)  R*  R+  R,  R-  R.  (    (    (    sC   lib/python2.7/site-packages/sympy/stats/tests/test_continuous_rv.pyt   <module>   s    ôÿ U"																			
				
																
												
									
					
	$				
		