Reparameterised zero-truncated negative binomial distribution

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.

Value

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

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.

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)