a
    \:b                  
   @   st  d Z ddlZdd Zdd ZedZedZed	Zed
Z	edZ
edZedZeee	eee	Zeee eeeeed d e eeed d edeed    e eeed d eeed  deeej   Zed d ede
e d e e   dee  Zed d ede
d e   d Zee Zeee eee
 ee eZee eee ed eed D ]\ZZeede qeeed d  ed ee Zeee eee
 ed eeeddddd eeeddddd  dS )z9
Created on Sat Mar 13 07:56:22 2010

Author: josef-pktd
    Nc                 C   s8   d|t dt j   t | | d  d|d    S )z=Return the probability density function as an expression in x      )sysqrtpiZexpxmusigma r   Hlib/python3.9/site-packages/statsmodels/sandbox/regression/sympy_diff.pypdf
   s    r   c                 C   s$   dt | | |t d   d S )z<Return the cumulative density function as an expression in xr   r   )r   Zerfr   r   r   r   r   cdf   s    r   r	   r
   sigma2r   ydfsr   r   g       @g      ?g      ?z0
 derivative of loglike of t distribution wrt df=z(
standard t distribution, dll_df, dll_dy
g      ?guq $@)r   r	   r   r   ) __doc__Zsympyr   r   r   ZSymbolr	   r
   r   r   r   r   r   logZdiffZdldxnormprintZsimplifyZgammar   Ztllf1Ztllf2Ztllf2stdZtllfZdlddfZcsekvZtllfstdZsubsdictZevalfr   r   r   r   <module>   sD   

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$.@8&