extraDistr (version 1.10.0)

ZIP: Zero-inflated Poisson distribution

Description

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

Usage

dzip(x, lambda, pi, log = FALSE)
pzip(q, lambda, pi, lower.tail = TRUE, log.p = FALSE)
qzip(p, lambda, pi, lower.tail = TRUE, log.p = FALSE)
rzip(n, lambda, pi)

Arguments

x, q

vector of quantiles.

lambda

vector of (non-negative) means.

pi

probability of extra zeros.

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\) otherwise, \(P[X > x]\).

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

Details

Probability density function $$ f(x) = \left\{\begin{array}{ll} \pi + (1 - \pi) e^{-\lambda} & x = 0 \\ (1 - \pi) \frac{\lambda^{x} e^{-\lambda}} {x!} & x > 0 \\ \end{array}\right. $$

See Also

Poisson

Examples

x <- rzip(1e5, 6, 0.33)
xx <- -2:20
plot(prop.table(table(x)), type = "h")
lines(xx, dzip(xx, 6, 0.33), col = "red")

xx <- seq(0, 20, by = 0.01)
plot(ecdf(x))
lines(xx, pzip(xx, 6, 0.33), col = "red")