Skellam {extraDistr}

Skellam distribution

Description

Probability mass function and random generation for the Skellam distribution.

Usage

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

f(x) = e^{-(\mu_1\!+\!\mu_2)} \left(\frac{\mu_1}{\mu_2}\right)^{k/2}\!\!I_{k}(2\sqrt{\mu_1\mu_2})

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.

Examples

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