Zero-truncated Negative Binomial distribution

Probability mass function, distribution function, and random generation for the zero-truncated Negative Binomial distribution.

Usage

dztnbinom(x, size, prob, log = FALSE)

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

rztnbinom(n, size, prob)

Arguments

x, q

integer vector of counts

size

target for number of successful trials, or dispersion parameter (the shape parameter of the gamma mixing distribution). Must be strictly positive, need not be integer.

prob

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

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

dztnbinom gives the probability mass function, pztnbinom gives the distribution function, and rztnbinom 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 <- rztnbinom(1, size = 2, prob = 0.5)
d <- dztnbinom(x, size = 2, prob = 0.5)
p <- pztnbinom(x, size = 2, prob = 0.5)