ztnbinom2: Reparameterised zero-truncated negative binomial distribution

In RTMBdist: Distributions Compatible with Automatic Differentiation by 'RTMB'

Reparameterised zero-truncated negative binomial distribution

Description

Probability mass function, distribution function, quantile function, and random generation for the zero-truncated negative binomial distribution reparameterised in terms of mean and size.

Usage

dztnbinom2(x, mu, size, log = FALSE)

pztnbinom2(q, mu, size, lower.tail = TRUE, log.p = FALSE)

rztnbinom2(n, mu, size)

Arguments

x, q	integer vector of counts
mu	mean parameter, must be positive
size	size/dispersion parameter, must be positive
log, log.p	logical; return log-density if TRUE
lower.tail	logical; if TRUE, probabilities are P[X \le x], otherwise, P[X > x].
n	number of random values to return.

Details

This implementation allows for automatic differentiation with RTMB.

By definition, this distribution only has support on the positive integers (1, 2, ...). Any zero-truncated distribution is defined as

P(X=x | X>0) = P(X=x) / (1 - P(X=0)),

where P(X=x) is the probability mass function of the corresponding untruncated distribution.

Value

dztnbinom2 gives the probability mass function, pztnbinom2 gives the distribution function, and rztnbinom2 generates random deviates.

Examples

set.seed(123)
x <- rztnbinom2(1, mu = 2, size = 1)
d <- dztnbinom2(x, mu = 2, size = 1)
p <- pztnbinom2(x, mu = 2, size = 1)

RTMBdist documentation built on April 1, 2026, 5:07 p.m.