ZIP: Zero-inflated Poisson distribution

In extraDistr: Additional Univariate and Multivariate Distributions

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")

extraDistr documentation built on May 29, 2024, 9:31 a.m.