extraDistr (version 1.10.0)

Skellam: 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")