Skellam distribution

Probability mass function, distribution function, and random generation for the Skellam distribution.

Usage

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

rskellam(n, mu1, mu2)

Arguments

x

integer vector of counts

mu1, mu2

Poisson means

log

logical; return log-density if TRUE

n

number of random values to return.

Value

dskellam gives the probability mass function and rskellam generates random deviates.

Details

The Skellam distribution is the distribution of the difference of two Poisson random variables. Specifically, if \(X_1 \sim \text{Pois}(\mu_1)\) and \(X_2 \sim \text{Pois}(\mu_2)\), then \(X_1 - X_2 \sim \text{Skellam}(\mu_1, \mu_2)\).

This implementation of dskellam allows for automatic differentiation with RTMB.

Examples

x <- rskellam(1, 2, 3)
d <- dskellam(x, 2, 3)