Zero-inflated Poisson distribution

Probability mass function, distribution function, and random generation for the zero-inflated Poisson distribution.

Usage

dzipois(x, lambda, zeroprob = 0, log = FALSE)

pzipois(q, lambda, zeroprob = 0, lower.tail = TRUE, log.p = FALSE)

rzipois(n, lambda, zeroprob = 0)

x, q: integer vector of counts
lambda: vector of (non-negative) means
zeroprob: zero-inflation probability between 0 and 1
log, log.p: logical; return log-density if TRUE
lower.tail: logical; if TRUE, probabilities are $P[X \le x]$, otherwise, $P[X > x]$.
n: number of random values to return.

dzipois gives the probability mass function, pzipois gives the distribution function, and rzipois generates random deviates.

This implementation allows for automatic differentiation with RTMB.

$$P(X=k;\,\lambda,p_0) = p_0\,\mathbf{1}[k=0] + (1-p_0)\,P_{\mathrm{Pois}}(k;\,\lambda),$$ where $p_0$ is zeroprob.

set.seed(123)
x <- rzipois(1, 0.5, 1)
d <- dzipois(x, 0.5, 1)
p <- pzipois(x, 0.5, 1)