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                  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            j                  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j                  e              eej                  e
             eez
  j                  e      Z ee        e ej2                  e              ed        ej2                  e      d   D ]  \  ZZ eede         e ej2                  e      d   d           ed       eez
  Z eej                  e              eej                  e
              ed        eej;                   edddd                    eej;                   edddd            j?                                y)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      f/var/www/dash_apps/app1/venv/lib/python3.12/site-packages/statsmodels/sandbox/regression/sympy_diff.pypdfr   	   sJ     eBGGAbeeG$$%2	zQuaxZ/H(III    c                 p    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      s3     bffadU2771:-.//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 $@)r   r   r   r   ) __doc__sympyr   r   r   Symbolr   r   r   r   r   r   r   logdiffdldxnormprintsimplifygammar   tllf1tllf2tllf2stdtllfdlddfcsekvtllfstdsubsdictevalf r   r   <module>r0      s)  
 J
3 RYYt_		'	8	BIIcNBIIcNRYYt_BIIcN266#aE"#((+ kbkk(  gbggfbffXRXXqsAg&'* + gbggr!tRi&"&&2r!t9--r2 3 	xrxxAr	"#fbffXRXXbe_&==FBFFBPRPUPU:DV@VV	B
VRVVB!B$B!6677#v:NNrE2:rAqDG|,,s2u} ejjn  ejjm 	u2 e fbffUm  9 :266%= CAa	!S! fbffUmAq  1 2
(
 gll2  gll1o  d ejjQcW56 7 ejjQcW56<<> ?r   