
    !g              	       ^   d Z ddlZddlmZ ddlmZ ddlm	Z
 ddlmc mZ ddlmc mc mZ  ej&                  g dg dg dg      Z ej&                  g d      Z ej,                  ee      Zej1                  d	      Zg d
g dg dg dgZ ej6                  e      j8                  dddddf   Zg dZg dZeD  cg c]  } ejA                  |        c} Z! eee!d        e"e!        e"d        e"e ej&                  ed         k  jG                  d      jI                  d              e"ed   ek  jG                  d      jI                  d              e"ejK                  d d	              e"ejK                  d d	             ejM                         Z' ee'jP                  e'jR                  d        ee'jH                   ejT                  d      d       ejW                  e      Z, ejP                  e,d      Z- ee'jP                  e-d        e ejT                  d      e,jI                  d      d       ej]                         Z/ ee'jP                  e/jP                  d       eja                  e      Z1 ejP                  e,d      Z2 eejR                  e2d        e ejT                  d      e1jI                  d      d       ejg                   ej&                  ddg            Z4 e"e4jH                          e"e4jP                         ejk                   ej&                  ddg      dg      Z6 e"e6jH                          e"e6jP                         ejk                   ej&                  dg      ddg      Z6 e"e6jH                          e"e6jP                          e
jn                  edddf    e
jp                  eddddf   d            Z9e9ju                         Z; e"e;jx                  j{                   ej&                  g d                   ejk                   ej&                  dg      ddg      Z6 e"e6jH                         ejk                   ej&                  dg      ddg      Z6 e"e;jx                  j{                   ej&                  g d                     e"e6jH                          ej|                  eed      Z?e?j1                  d	      Z@ ee?jP                   ejP                  e@d      d       e?j                         ZBe?jM                         ZC ee?jR                  eCj                  d        eeCjR                  eCj                  d        e ej                  d      eBj                  d       e?ja                  e@      ZF ejP                  eFd      ZGe?jW                  e@      ZH ejP                  eHd      ZI ej                  eHd      ZK eeCjH                  eHjI                  d      d        eeCjR                  eKd        eeCjP                  eId        eeBjP                  eGd       g dZLe?jA                  eL      ZM e"eM        e"e@ ej&                  eL      k  jG                  d      jI                  d              e"d!d"        e"d!d#        e"d$eMd#z
         g d%ZLe?jA                  eL      ZN e"eN        e"e@ ej&                  eL      k  jG                  d      jI                  d              e"d!d&        e"d!d'        e"d$eNd'z
          eeMd#d(        eeNd'd(        ej&                  g d)      ZO ej,                  eOed*z  d      ZP ej                  d+d,gd(e?eCgd      ZR ej                  d+d,gd-eePgd      Z ej                         ZTeTj                  ddd        ej                  edddf   edddf   d.d/0        ej                  d1       eTj                  ddd        ej                  edddf   edddf   d.d/0        ej                  d2       eTj                  ddd        ej                  edddf   edddf   d.d/0        ej                  d3       yc c} w )4zexamples for multivariate normal and t distributions


Created on Fri Jun 03 16:00:26 2011

@author: josef


for comparison I used R mvtnorm version 0.9-96

    N)assert_array_almost_equal)      ?      ?      ?)r         ?333333?)r   r          @)        r	   i@B )size)r	   r   r   )r   r	   r   )r   r   g      @)r   r   r   )gT=8g?gP?g,i q?gG?)g>g!>gkU?g!(H?   )decimal r
   .N   c                 8    | t         d   k  j                  d      S )Nr   r
   )xliallxs    w/var/www/dash_apps/app1/venv/lib/python3.12/site-packages/statsmodels/sandbox/distributions/examples/ex_mvelliptical.py<lambda>r   4   s    #a&~~b1     i c                 8    | d   t         k  j                  d      S )Nr   r   )xliarrr   r   s    r   r   r   5   s    (F 277: r         )rowvar   T)prepend)r   r   r   )r   r   r   Rg(60_?gQL 3_?diff)r   r   r   g?g$K&]?   )r   r	   r	   r	   g?r   i  .g      ?)alphaz
1 versus 0z
2 versus 0z
2 versus 1)X__doc__numpynpnumpy.testingr   matplotlib.pyplotpyplotpltstatsmodels.apiapism%statsmodels.distributions.mixture_rvsdistributionsmixture_rvsmix+statsmodels.sandbox.distributions.mv_normalsandbox	mv_normalmvdarraycov3muMVNormalmvn3rvsr   r   asarrayTr   r_cdfr_cdf_errorscdfn_cdfprintr   mean	expect_mc
normalizedmvn3ncovcorrzeros	normalizexnxn_covnormalized2mvn3n2standardizexsxs_covmarginalmv2mconditionalmv2cOLSadd_constantmodfitresmodelpredictMVTmvt3xtstandardizedmvt3smvt3nsigmaeyextsxts_covxtnxtn_covcorrcoefxtn_corra	mvt3_cdf0	mvt3_cdf1mu2mvn32mv_mixture_rvsmdfigurefigadd_subplotplottitle)rm   s   0r   <module>ry      s_  
  3   3 3 9 9 rxx&((* + RXXn s||B 	HH'H
 
C		419	% 	5G!"!" % 2 e b	 q#a&	r"''* + q{6q!&&q) * dnn1n? @ dnn:nH I 	 %))UZZ < %**hbhhqk2 >	^^A	1	 %))VQ 7 ("((1+rwwqz1 =				 %))VZZ ; 
a	1	 $))VQ 7 ("((1+rwwqz1 =}}XRXXqe_% dii  dhh!A!- dii  dhh!1v. dii  dhhbffQqsV_R__QqtWd;<	ggi cii)* +!1v. dii !1v. cii)* + dii  swwr4	XX6X $((FBFF2a$8! D $))U[[" = %**ekk2 > &"&&)U[[" =
r
"&&Q

nnR
"&&Q
2;;s1% %**chhqk1 = %**h : %))Wa 8 %))Wa 8HHQK	 i  r("((1+~2##A& ' c9  c9  fi)# $HHQK	 i  r("((1+~2##A& ' c9  c9  fi)# $ )Y : )Y :bhh}S$r'1%Sc
Ae}a8c#sTD%=!<cjjl 1a  QqS3qs8S - 			,  1a  QqS3qs8S - 			,  1a  QqS3qs8S - 			, i 	#s   b*