Sympy stats.GeneralizedMultivariateLogGamma() in Python

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

Syntax : GeneralizedMultivariateLogGamma(syms, delta, v, lamda, mu)
Parameters :
1) Syms – list of symbols
2) Delta – a constant in range [0, 1]
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.GeneralizedMultivariateLogGamma() method, we are able to get the continuous joint random variable representing Generalized Multivariate Log Gamma distribution by using this method.

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

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

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

pprint(gfg)

Output :

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

Example #2 :

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

v = 1
l, mu = [1, 2, 3], [2, 5, 1]
d = S.One
y = symbols('y_1:4', positive = True)

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

pprint(gfg)

Output :

   oo                                                                        
______                                                                       
\     `                                                                      
 \                                                               5*y_2    y_3
  \                                                     2*y_1   e        e   
   \                   (n + 1)*(2*y_1 + 5*y_2 + y_3) - e      - ------ - ----
    \       n  -n - 1                                             2       3  
    /   10*0 *6      *e                                                      
   /    ---------------------------------------------------------------------
  /                                      3                                   
 /                                  Gamma (n + 1)                            
/_____,                                                                      
 n = 0