With the help of sympy.stats.Skellam() method, we can create a discrete random variable with a Skellam distribution.
The Skellam is the distribution of the difference N1 – N2 of two statistically independent random variables N1 and N2 each Poisson-distributed with respective expected values mu1 and mu2.
Syntax: sympy.stats.Skellam(name, mu1, mu2) Parameters: mu1: A non-negative value mu2: A non-negative value Returns: discrete random variable with a Skellam distribution.
Example #1 :
Python3
# import sympy, Skellam, density, Symbol from sympy.stats import Skellam, density from sympy import Symbol mu1 = Symbol("mu1", positive = True) mu2 = Symbol("mu2", positive = True) # using sympy.stats.Skellam() method X = Skellam("x", mu1, mu2) skeDist = density(X)(z) print(skeDist) |
Output:
(mu1/mu2)**(z/2)*exp(-mu1 - mu2)*besseli(z, 2*sqrt(mu1)*sqrt(mu2))
Example #2 :
Python3
# import sympy, Skellam, density from sympy.stats import Skellam, density # using sympy.stats.Skellam() method X = Skellam("x", 1, 2) skeDist = density(X)(3) print(skeDist) |
Output:
sqrt(2)*exp(-3)*besseli(3, 2*sqrt(2))/4
