sympy.stats.NegativeMultinomial() function in Python

With the help of sympy.stats.NegativeMultinomial() method, we can create a discrete random variable with Negative Multinomial Distribution.

Syntax: sympy.stats.NegativeMultinomial(syms, k, p)

Parameters: 
 syms: the symbol
 k: number of failures before the experiment is stopped, a positive integer
 p: event probabilites, p>= 0 and p<= 1

Returns: a discrete random variable with Negative Multinomial Distribution.

Example #1 :

Python3

# import sympy, NegativeMultinomia, density, symbols
from sympy.stats import density
from sympy.stats.joint_rv_types import NegativeMultinomial
from sympy import symbols, pprint

p1, p2, p3 = symbols('p1, p2, p3', positive = True)
x1, x2, x3 = symbols('x1, x2, x3', nonnegative = True, integer = True)

# using sympy.stats.NegativeMultinomial() method
N = NegativeMultinomial('N', 3, p1, p2, p3)
negMulti = density(N)(x1, x2, x3)

pprint(negMulti)

Output :

  x1   x2   x3                    3                        
p1  *p2  *p3  *(-p1 - p2 - p3 + 1) *Gamma(x1 + x2 + x3 + 3)
-----------------------------------------------------------
                       2*x1!*x2!*x3!   

Example #2 :

Python3

# import sympy, NegativeMultinomia, density, symbols
from sympy.stats import density
from sympy.stats.joint_rv_types import NegativeMultinomial
from sympy import symbols, pprint

x1, x2, x3 = symbols('x1, x2, x3', nonnegative = True, integer = True)

# using sympy.stats.NegativeMultinomial() method
N = NegativeMultinomial('N', 2, 1 / 3, 1 / 2)
negMulti = density(N)(x1, x2, x3)

pprint(negMulti)

Output :

 -x2  -x1                        
2   *3   *Gamma(x1 + x2 + x3 + 2)
---------------------------------
            36*x1!*x