U
    Ãmœd  ã                   @   s’  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  mZ ddlm  m  mZ e dddgdddgddd	gg¡Ze d
dd	g¡Ze ee¡Zejdd�Zd	ddgdd	dgdddgdddggZe e¡jddd…dd…f ZddddgZddddgZdd„ eD ƒZ eee dd� e!e ƒ e!dƒ e!ee ed ¡k  "d
¡ #d¡ƒ e!ed ek  "d¡ #d¡ƒ e!ej$dd„ d d�ƒ e!ej$d!d„ d d�ƒ e %¡ Z&ee&j'e&j(d"d� ee&j#e )d#¡d"d� e *e¡Z+ej'e+dd$�Z,ee&j'e,d%d� ee )d#¡e+ #d¡d%d� e -¡ Z.ee&j'e.j'd%d� e /e¡Z0ej'e+dd$�Z1eej(e1d%d� ee )d#¡e0 #d¡d%d� e 2e ddg¡¡Z3e!e3j#ƒ e!e3j'ƒ e 4e ddg¡dg¡Z5e!e5j#ƒ e!e5j'ƒ e 4e dg¡ddg¡Z5e!e5j#ƒ e!e5j'ƒ e
 6edd…df e
j7edd…dd…f d&d'�¡Z8e8 9¡ Z:e!e:j; <e dddg¡¡ƒ e 4e dg¡ddg¡Z5e!e5j#ƒ e 4e dg¡ddg¡Z5e!e:j; <e dddg¡¡ƒ e!e5j#ƒ e =eed¡Z>e>jd d�Z?ee>j'ej'e?dd$�dd� e> @¡ ZAe> %¡ ZBee>j(eBjCd"d� eeBj(eBjCd"d� ee Dd#¡eAjCd"d� e> /e?¡ZEej'eEdd$�ZFe> *e?¡ZGej'eGdd$�ZHejIeGdd$�ZJeeBj#eG #d¡d%d� eeBj(eJdd� eeBj'eHdd� eeAj'eFdd� dddgZKe> LeK¡ZMe!eMƒ e!e?e eK¡k  "d
¡ #d¡ƒ e!d(d)ƒ e!d(d*ƒ e!d+eMd* ƒ dddgZKe> LeK¡ZNe!eNƒ e!e?e eK¡k  "d
¡ #d¡ƒ e!d(d,ƒ e!d(d-ƒ e!d+eNd- ƒ eeMd*d.d� eeNd-d.d� e dd	d	g¡ZOe eOed	 d¡ZPe Qd/dgd.e>eBgd#¡ZRe Qd/dgd0eePgd#¡Ze S¡ ZTeT Ud%d%d¡ ejVedd…df edd…df d1d2d3� e Wd4¡ eT Ud%d%d%¡ ejVedd…df edd…d%f d1d2d3� e Wd5¡ eT Ud%d%d#¡ ejVedd…df edd…d%f d1d2d3� e Wd6¡ dS )7z�examples 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

é    N)Úassert_array_almost_equalg      ð?g      à?g      è?g      ø?g333333ã?g       @éÿÿÿÿg        i@B )Úsizeg      @gT=ô8gŸÔ?gP�ÚÕ?g„,i qá?gÃËG½ñÓ?gÅø˜½úûñ>gó!ê×â¬ð>g¶ÞkU?g½!±(H´?c                 C   s   g | ]}t  |¡‘qS © )Úmvn3Úcdf)Ú.0Úar   r   ús/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/statsmodels/sandbox/distributions/examples/ex_mvelliptical.pyÚ
<listcomp>.   s     r   é   )ÚdecimalÚ ©.Né   c                 C   s   | t d k  d¡S )Nr   r   )ÚxliÚall©Úxr   r   r
   Ú<lambda>5   ó    r   i † c                 C   s   | d t k  d¡S )Nr   r   )Úxliarrr   r   r   r   r
   r   6   r   é   é   )Zrowvaré   T)ÚprependÚRg±(60_Ó?gQLÞ 3_Ó?Údiffg²¥¢°êÈ?g$ÄK&]éÈ?é   gš™™™™™Ù?iÐ  Ú.g      Ð?)Úalphaz
1 versus 0z
2 versus 0z
2 versus 1)XÚ__doc__ÚnumpyÚnpZnumpy.testingr   Zmatplotlib.pyplotZpyplotZpltZstatsmodels.apiÚapiÚsmZ%statsmodels.distributions.mixture_rvsÚdistributionsZmixture_rvsZmixZ+statsmodels.sandbox.distributions.mv_normalZsandboxZ	mv_normalZmvdÚarrayZcov3ÚmuZMVNormalr   Zrvsr   r   ZasarrayÚTr   Zr_cdfZr_cdf_errorsZn_cdfÚprintr   ZmeanZ	expect_mcÚ
normalizedZmvn3nZcovZcorrZzerosÚ	normalizeZxnZxn_covZnormalized2Zmvn3n2ZstandardizeZxsZxs_covZmarginalZmv2mZconditionalZmv2cZOLSZadd_constantÚmodÚfitÚresÚmodelZpredictZMVTZmvt3ZxtZstandardizedZmvt3sZmvt3nÚsigmaÚeyeZxtsZxts_covZxtnZxtn_covZcorrcoefZxtn_corrr	   r   Z	mvt3_cdf0Z	mvt3_cdf1Zmu2Zmvn32Zmv_mixture_rvsÚmdZfigureZfigZadd_subplotZplotÚtitler   r   r   r
   Ú<module>   sÔ   þý"







2











*
*
*