sympy.stats.NormalGamma() function in Python

With the help of sympy.stats.NormalGamma() method, we can create a bivariate joint random variable with multivariate Normal gamma distribution.

Syntax:  sympy.stats.NormalGamma(syms, mu, lamda, alpha, beta)
 
Parameters:
 syms: the symbol, for identifying the random variable
 mu: a real number, the mean of the normal distribution
 lambda: a positive integer
 alpha: a positive integer
 beta: a positive integer

Returns:  a bivariate joint random variable with multivariate Normal gamma distribution.

Example #1 :

Python3

# import sympy, NormalGamma, density, symbols
from sympy.stats import density, NormalGamma
from sympy import symbols, pprint

y, z = symbols('y z')

# using sympy.stats.NormalGamma() method
X = NormalGamma('X', 0, 1, 2, 3)
norGammaDist = density(X)(y, z)

pprint(norGammaDist)

Output :

                      2   
                    -y *z 
                    ------
    ___  3/2  -3*z    2   
9*\/ 2 *z   *e    *e      
--------------------------
             ____         
         2*\/ pi      

Example #2 :

Python3

# import sympy, NormalGamma, density, symbols
from sympy.stats import density, NormalGamma
from sympy import symbols, pprint

y, z = symbols('y z')

# using sympy.stats.NormalGamma() method
X = NormalGamma('X', 1 / 2, 3, 4, 6)
norGammaDist = density(X)(y, z)

pprint(norGammaDist)

Output :

                                    2 
                      -3*z*(y - 1/2)  
                      ----------------
      ___  7/2  -6*z         2        
108*\/ 6 *z   *e    *e                
--------------------------------------
                  ____                
                \/ pi