scipy.stats._discrete_distns:skellam_gen

Notes

Probability distribution of the difference of two correlated or uncorrelated Poisson random variables.

Let $k_1$ and $k_2$ be two Poisson-distributed r.v. with expected values ${\lambda }_1$ and ${\lambda }_2$. Then, $k_1-k_2$ follows a Skellam distribution with parameters ${\mu }_1={\lambda }_1-\rho \sqrt{{\lambda }_1{\lambda }_2}$ and ${\mu }_2={\lambda }_2-\rho \sqrt{{\lambda }_1{\lambda }_2}$, where $\rho$ is the correlation coefficient between $k_1$ and $k_2$. If the two Poisson-distributed r.v. are independent then $\rho =0$.

Parameters ${\mu }_1$ and ${\mu }_2$ must be strictly positive.

skellam takes ${\mu }_1$ and ${\mu }_2$ as shape parameters.

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