# sympy.stats.Skellam() function in Python

• Last Updated : 18 Aug, 2020

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
```
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