extraDistr (version 1.9.1)

ZIB: Zero-inflated binomial distribution

Description

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

Usage

dzib(x, size, prob, pi, log = FALSE)
pzib(q, size, prob, pi, lower.tail = TRUE, log.p = FALSE)
qzib(p, size, prob, pi, lower.tail = TRUE, log.p = FALSE)
rzib(n, size, prob, pi)

Arguments

x, q

vector of quantiles.

size

number of trials (zero or more).

prob

probability of success in each trial. 0 < prob <= 1.

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 $$ f(x) = \left\{\begin{array}{ll} \pi + (1 - \pi) (1-p)^n & x = 0 \\ (1 - \pi) {n \choose x} p^x (1-p)^{n-x} & x > 0 \\ \end{array}\right. $$

See Also

Binomial

Examples

x <- rzib(1e5, 10, 0.6, 0.33)
xx <- -2:20
plot(prop.table(table(x)), type = "h")
lines(xx, dzib(xx, 10, 0.6, 0.33), col = "red")

xx <- seq(0, 20, by = 0.01)
plot(ecdf(x))
lines(xx, pzib(xx, 10, 0.6, 0.33), col = "red")