Sympy stats.GeneralizedMultivariateLogGammaOmega() in python

With the help of sympy.stats.GeneralizedMultivariateLogGammaOmega() method, we can get the continuous joint random variable which represents the extended Generalized Multivariate Log Gamma distribution.

Syntax : GeneralizedMultivariateLogGammaOmega(syms, omega, v, lamda, mu)
Parameters :
1) Syms – list of symbols
2) Omega – a square matrix
3) V – positive real number
4) Lambda – a list of positive reals
5) mu – a list of positive real numbers.
Return : Return the continuous joint random variable.

Example #1 :
In this example we can see that by using sympy.stats.GeneralizedMultivariateLogGammaOmega() method, we are able to get the continuous joint random variable representing extended Generalized Multivariate Log Gamma distribution by using this method.

# Import sympy and GeneralizedMultivariateLogGammaOmega
from sympy.stats import density
from sympy.stats.joint_rv_types import GeneralizedMultivariateLogGammaOmega
from sympy.stats.joint_rv import marginal_distribution
from sympy import symbols, S, Matrix

v = 1
l, mu = [1, 1, 1], [1, 1, 1]
d = S.One
y = symbols('y_1:4', positive = True)
omega = Matrix([[1, S.Half, S.Half], [S.Half, 1, S.Half], [S.Half, S.Half, 1]])

# Using sympy.stats.GeneralizedMultivariateLogGammaOmega() method
Gd = GeneralizedMultivariateLogGammaOmega('G', omega, v, l, mu)
gfg = density(Gd)(y[0], y[1], y[2])

pprint(gfg)

Output :

         oo                                                               
      ______                                                              
      \     `                                                             
       \                 n                                                
        \     /      ___\                                y_1    y_2    y_3
         \    |    \/ 2 |   (n + 1)*(y_1 + y_2 + y_3) - e    - e    - e   
  ___     \   |1 - -----| *e                                              
\/ 2 *    /   \      2  /                                                 
         /    ------------------------------------------------------------
        /                                 3                               
       /                             Gamma (n + 1)                        
      /_____,                                                             
       n = 0                                                              
--------------------------------------------------------------------------
                                    2                                     

Example #2 :

# Import sympy and GeneralizedMultivariateLogGammaOmega
from sympy.stats import density
from sympy.stats.joint_rv_types import GeneralizedMultivariateLogGammaOmega
from sympy.stats.joint_rv import marginal_distribution
from sympy import symbols, S, Matrix

v = 1
l, mu = [1, 2], [2, 1]
d = S.One
y = symbols('y_1:3', positive = True)
omega = Matrix([[1, S.Half], [S.Half, 1]])

# Using sympy.stats.GeneralizedMultivariateLogGammaOmega() method
Gd = GeneralizedMultivariateLogGammaOmega('G', omega, v, l, mu)
gfg = density(Gd)(y[0], y[1])

pprint(gfg)

Output :

     oo                                                       
  ______                                                      
  \     `                                                     
   \                                                       y_2
    \                                             2*y_1   e   
     \                   (n + 1)*(2*y_1 + y_2) - e      - ----
      \      -n - 1  -n                                    2  
3*    /   2*2      *4  *e                                     
     /    ----------------------------------------------------
    /                             2                           
   /                         Gamma (n + 1)                    
  /_____,                                                     
   n = 0                                                      
--------------------------------------------------------------
                              4