Skellam function

Skellam distribution

Probability mass function and random generation for the Skellam distribution.

dskellam(x, mu1, mu2, log = FALSE)

rskellam(n, mu1, mu2)

Arguments

• x: vector of quantiles.
• mu1, mu2: positive valued parameters.
• log: logical; if TRUE, probabilities p are given as log(p).
• n: number of observations. If length(n) > 1, the length is taken to be the number required.

Details

If $X$ and $Y$ follow Poisson distributions with means $\mu[1]$ and $\mu[2]$, than $X-Y$ follows Skellam distribution parametrized by $\mu[1]$ and $\mu[2]$.

Probability mass function

Examples

x <- rskellam(1e5, 5, 13)
xx <- -40:40
plot(prop.table(table(x)), type = "h")
lines(xx, dskellam(xx, 5, 13), col = "red")

References

Karlis, D., & Ntzoufras, I. (2006). Bayesian analysis of the differences of count data. Statistics in medicine, 25(11), 1885-1905.

Skellam, J.G. (1946). The frequency distribution of the difference between two Poisson variates belonging to different populations. Journal of the Royal Statistical Society, series A, 109(3), 26.