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

Author: josef-pktd
    Nc                     d|t          j        dt           j        z            z  z  t          j        | |z
  dz   d|dz  z  z            z  S )z=Return the probability density function as an expression in x      )sysqrtpiexpxmusigmas      i/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/sandbox/regression/sympy_diff.pypdfr   	   sJ     eBGAbeG$$$%2	zQuaxZ/H(I(III    c                 l    dt          j        | |z
  |t          j        d          z  z            z   dz  S )z<Return the cumulative density function as an expression in xr   r   )r   erfr   r
   s      r   cdfr      s4     bfadU271::-.///22r   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 $@)r   r   r   r   ) __doc__sympyr   r   r   Symbolr   r   r   r   r   r   r   logdiffdldxnormprintsimplifygammar   tllf1tllf2tllf2stdtllfdlddfcsekvtllfstdsubsdictevalf r   r   <module>r0      s	   
    J J J
3 3 3 RYt__	'	8		BIcNNBIcNNRYt__BIcNN26##aE""##((++ kbk(    gbgfbfXRXqsAg&&''** + + + gbgr!tRi&"&2r!t9---r22 3 3 3 	xrxAr	""##fbfXRXbe__&=&==FBFBPRPU:DVDV@VV	B
VRVB!B$B!66777#v:NNrE2:rAqDG|,,,s2u} ejjnn    ejjmm   	u2 e fbfUmm    9 : : :26%==  CAa	E!S! fbfUmmAq    1 2 2 2
(
 gll2    gll1oo    d ejjQcW55566 7 7 7 ejjQcW55566<<>> ? ? ? ? ?r   