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.