Skellam distribution
Probability mass function and random generation for the Skellam distribution.
dskellam(x, mu1, mu2, log = FALSE) rskellam(n, mu1, mu2)
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 |
If X and Y follow Poisson distributions with means μ[1] and μ[2], than X-Y follows Skellam distribution parametrized by μ[1] and μ[2].
Probability mass function
f(x) = exp(-(μ1+μ2)) * (μ1/μ2)^(x/2) * besselI(2*sqrt(μ1*μ2), x)
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.
x <- rskellam(1e5, 5, 13) xx <- -40:40 plot(prop.table(table(x)), type = "h") lines(xx, dskellam(xx, 5, 13), col = "red")
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