nbinom2: Reparameterised negative binomial distribution

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

Reparameterised negative binomial distribution

Description

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

Usage

dnbinom2(x, mu, size, log = FALSE)

pnbinom2(q, mu, size, lower.tail = TRUE, log.p = FALSE)

qnbinom2(p, mu, size, lower.tail = TRUE, log.p = FALSE)

rnbinom2(n, mu, size)

Arguments

x, q	vector of quantiles
mu	mean parameter, must be positive.
size	size parameter, must be positive.
log, log.p	logical; if TRUE, probabilities/ densities p are returned as \log(p).
lower.tail	logical; if TRUE, probabilities are P[X \le x], otherwise, P[X > x].
p	vector of probabilities
n	number of random values to return.

Details

This implementation allows for automatic differentiation with RTMB.

pnbinom is an AD-compatible implementation of the standard parameterisation of the CDF, missing from RTMB.

Reparameterises the negative binomial by mean \mu via p = r/(r+\mu):

P(X=k;\,\mu,r) = \binom{k+r-1}{k}\left(\frac{r}{r+\mu}\right)^r\left(\frac{\mu}{r+\mu}\right)^k, \quad k = 0,1,2,\ldots

Value

dnbinom2 gives the density, pnbinom2 gives the distribution function, qnbinom2 gives the quantile function, and rnbinom2 generates random deviates.

Examples

set.seed(123)
x <- rnbinom2(1, 1, 2)
d <- dnbinom2(x, 1, 2)
p <- pnbinom2(x, 1, 2)
q <- qnbinom2(p, 1, 2)

RTMBdist documentation built on Oct. 31, 2026, 5:07 p.m.