zinbinom: The zero-inflated negative binomial distribution

In distributions3: Probability Distributions as S3 Objects

The zero-inflated negative binomial distribution

Description

Density, distribution function, quantile function, and random generation for the zero-inflated negative binomial distribution with parameters mu, theta (or size), and pi.

Usage

dzinbinom(x, mu, theta, size, pi, log = FALSE)

pzinbinom(q, mu, theta, size, pi, lower.tail = TRUE, log.p = FALSE)

qzinbinom(p, mu, theta, size, pi, lower.tail = TRUE, log.p = FALSE)

rzinbinom(n, mu, theta, size, pi)

Arguments

x	vector of (non-negative integer) quantiles.
mu	vector of (non-negative) negative binomial location parameters.
theta, size	vector of (non-negative) negative binomial overdispersion parameters. Only theta or, equivalently, size may be specified.
pi	vector of zero-inflation probabilities in the unit interval.
log, log.p	logical indicating whether probabilities p are given as log(p).
q	vector of quantiles.
lower.tail	logical indicating whether probabilities are P[X ≤ x] (lower tail) or P[X > x] (upper tail).
p	vector of probabilities.
n	number of random values to return.

Details

All functions follow the usual conventions of d/p/q/r functions in base R. In particular, all four zinbinom functions for the zero-inflated negative binomial distribution call the corresponding nbinom functions for the negative binomial distribution from base R internally.

Note, however, that the precision of qzinbinom for very large probabilities (close to 1) is limited because the probabilities are internally handled in levels and not in logs (even if log.p = TRUE).

See Also

ZINegativeBinomial, dnbinom

Examples

## theoretical probabilities for a zero-inflated negative binomial distribution
x <- 0:8
p <- dzinbinom(x, mu = 2.5, theta = 1, pi = 0.25)
plot(x, p, type = "h", lwd = 2)

## corresponding empirical frequencies from a simulated sample
set.seed(0)
y <- rzinbinom(500, mu = 2.5, theta = 1, pi = 0.25)
hist(y, breaks = -1:max(y) + 0.5)

distributions3 documentation built on Sept. 7, 2022, 5:07 p.m.