
    M/Ph              	          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                    d	          Zg d
g dg dg dgZ ej        e          j        dddddf         Zg dZg dZd eD             Z  eee d            e!e             e!d            e!e ej        ed                   k     "                    d          #                    d                      e!ed         ek     "                    d          #                    d                      e!e$                    d d	                      e!e$                    d d	                     e%                                Z& ee&j'        e&j(        d            ee&j#         ej)        d          d           e*                    e          Z+ ej'        e+d          Z, ee&j'        e,d            e ej)        d          e+#                    d          d           e-                                Z. ee&j'        e.j'        d           e/                    e          Z0 ej'        e+d          Z1 eej(        e1d            e ej)        d          e0#                    d          d           e2                     ej        ddg                    Z3 e!e3j#                    e!e3j'                   e4                     ej        ddg          dg          Z5 e!e5j#                    e!e5j'                   e4                     ej        dg          ddg          Z5 e!e5j#                    e!e5j'                    e
j6        edddf          e
j7        eddddf         d                    Z8e89                                Z: e!e:j;        <                     ej        g d                                e4                     ej        dg          ddg          Z5 e!e5j#                   e4                     ej        dg          ddg          Z5 e!e:j;        <                     ej        g d!                                e!e5j#                    ej=        eed          Z>e>                    d	          Z? ee>j'         ej'        e?d          d           e>@                                ZAe>%                                ZB ee>j(        eBjC        d            eeBj(        eBjC        d            e ejD        d          eAjC        d           e>/                    e?          ZE ej'        eEd          ZFe>*                    e?          ZG ej'        eGd          ZH ejI        eGd          ZJ eeBj#        eG#                    d          d            eeBj(        eJd            eeBj'        eHd            eeAj'        eFd           g dZKe>L                    eK          ZM e!eM            e!e? ej        eK          k     "                    d          #                    d                      e!d"d#            e!d"d$            e!d%eMd$z
             g d&ZKe>L                    eK          ZN e!eN            e!e? ej        eK          k     "                    d          #                    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jQ        d,d-gd)e>eBgd          ZR ejQ        d,d-gd.eePgd          Z ejS                    ZTeTU                    ddd            ejV        edddf         edddf         d/d01            ejW        d2           eTU                    ddd            ejV        edddf         edddf         d/d01            ejW        d3           eTU                    ddd            ejV        edddf         edddf         d/d01            ejW        d4           dS )5zexamples 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?c                 B    g | ]}t                               |          S  )mvn3cdf).0as     z/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/sandbox/distributions/examples/ex_mvelliptical.py
<listcomp>r   -   s"    """!"""       )decimal r
   .N   c                 J    | t           d         k                         d          S )Nr   r
   )xliallxs    r   <lambda>r    4   s    #a&~~b11 r   i c                 J    | d         t           k                         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$K&]?   )r   r	   r	   r	   g?r   i  .g      ?)alphaz
1 versus 0z
2 versus 0z
2 versus 1)X__doc__numpynpnumpy.testingr   matplotlib.pyplotpyplotpltstatsmodels.apiapism%statsmodels.distributions.mixture_rvsdistributionsmixture_rvsmix+statsmodels.sandbox.distributions.mv_normalsandbox	mv_normalmvdarraycov3muMVNormalr   rvsr   r   asarrayTr"   r_cdfr_cdf_errorsn_cdfprintr   mean	expect_mc
normalizedmvn3ncovcorrzeros	normalizexnxn_covnormalized2mvn3n2standardizexsxs_covmarginalmv2mconditionalmv2cOLSadd_constantmodfitresmodelpredictMVTmvt3xtstandardizedmvt3smvt3nsigmaeyextsxts_covxtnxtn_covcorrcoefxtn_corrr   r   	mvt3_cdf0	mvt3_cdf1mu2mvn32mv_mixture_rvsmdfigurefigadd_subplotplottitler   r   r   <module>r}      s[
  
 
     3 3 3 3 3 3             3 3 3 3 3 3 3 3 3 9 9 9 9 9 9 9 9 9 9 9 9 rx&&&((((((* + + RXnnn s|B 	HH'H}}}}~~}}
 
C	41119	% 	544GGG""c"""  % 2 2 2 2 e b			 q#a&		r""''** + + + q{6q!!&&q)) * * * dnn11n?? @ @ @ dnn::nHH I I I 	  %)UZ < < < <  %*hbhqkk2 > > > >	^^A	1			  %)VQ 7 7 7 7  ("(1++rwwqzz1 = = = =					  %)VZ ; ; ; ; 
a	1			  $)VQ 7 7 7 7  ("(1++rwwqzz1 = = = =}}XRXqe__%% di    dh!A!-- di    dh!1v.. di    dhbfQqqqsV_R_QqqqtWd;;;<<	ggii ci))** + + +!1v.. di   !1v.. ci))** + + + di    swr4	XX6X  $(FBF2a$8$8$8! D D D D  $)U[" = = = =  %*ek2 > > > >  &"&))U[" = = = =
r
"&Q



nnR
"&Q


2;s1%%%  %*chhqkk1 = = = =  %*h : : : :  %)Wa 8 8 8 8  %)Wa 8 8 8 8OOHHQKK	 i    r("(1++~2##A&& ' ' ' c9    c9    fi)# $ $ $OOHHQKK	 i    r("(1++~2##A&& ' ' ' c9    c9    fi)# $ $ $  )Y : : : :  )Y : : : :bh}}}S$r'1%%Sc
Ae}a88c#sTD%=!<<cjll 1a    QQQqS3qqqs8S - - - - 		,    1a    QQQqS3qqqs8S - - - - 		,    1a    QQQqS3qqqs8S - - - - 		,     r   