Skellam

class pymc_experimental.distributions.Skellam(name, mu1, mu2, **kwargs)

Skellam distribution.

The Skellam distribution is the distribution of the difference of two Poisson random variables.

The pmf of this distribution is

\[f(x | \mu_1, \mu_2) = e^{{-(\mu _{1}\!+\!\mu _{2})}}\left({\frac {\mu _{1}}{\mu _{2}}}\right)^{{x/2}}\!\!I_{{x}}(2{\sqrt {\mu _{1}\mu _{2}}})\]

where \(I_{x}\) is the modified Bessel function of the first kind of order \(x\).

Read more about the Skellam distribution at https://en.wikipedia.org/wiki/Skellam_distribution

(Source code, png, hires.png, pdf)

Support	\(x \in \mathbb{Z}\)
Mean	\(\mu_{1} - \mu_{2}\)
Variance	\(\mu_{1} + \mu_{2}\)

Parameters:

• mu1 (tensor_like of float) – Mean parameter (mu1 >= 0).

• mu2 (tensor_like of float) – Mean parameter (mu2 >= 0).

__init__()

Methods

__init__()
dist(mu1, mu2, **kwargs)
skellam_dist(mu1, mu2, size)
skellam_logp(value, mu1, mu2)