The zero-truncated negative binomial distribution

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

Usage

dztnbinom(x, mu, theta, size, log = FALSE)

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

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

rztnbinom(n, mu, theta, size)

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.

log, log.p

logical indicating whether probabilities p are given as log(p).

q

vector of quantiles.

lower.tail

logical indicating whether probabilities are \(P[X \le x]\) (lower tail) or \(P[X > x]\) (upper tail).

p

vector of probabilities.

n

number of random values to return.

Details

The negative binomial distribution left-truncated at zero (or zero-truncated negative binomial for short) is the distribution obtained, when considering a negative binomial variable Y conditional on Y being greater than zero.

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

See also

ZTNegativeBinomial, dnbinom

Examples

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


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