hnbinom: Hurdle negative binomial distribution

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

Hurdle negative binomial distribution

Description

Probability mass function, distribution function, and random generation for the hurdle (zero-altered) negative binomial distribution.

Usage

dhnbinom(x, size, prob, zeroprob = 0.5, log = FALSE)

phnbinom(q, size, prob, zeroprob = 0.5, lower.tail = TRUE, log.p = FALSE)

rhnbinom(n, size, prob, zeroprob = 0.5)

Arguments

x, q	integer vector of counts
size	dispersion parameter, must be strictly positive
prob	probability of success in each trial, in (0,1)
zeroprob	probability of a zero, between 0 and 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.

Details

This implementation allows for automatic differentiation with RTMB.

A hurdle distribution models the zeros and the positive counts as two separate processes: the probability of a zero is a free parameter, and the positive counts follow the corresponding zero-truncated distribution. Writing p_0 for zeroprob,

P(X = 0) = p_0, \qquad P(X = x) = (1 - p_0)\,\frac{P_{\mathrm{NB}}(x;\,r,\pi)}{1 - \pi_0}, \quad x = 1, 2, \ldots

where \pi_0 = P_{\mathrm{NB}}(0;\,r,\pi) is the probability of a zero under the ordinary negative binomial.

Unlike zero-inflation, which can only add zeros to those the negative binomial already produces, zeroprob here is exactly the probability of a zero and may be larger or smaller than \pi_0. The two coincide with the ordinary negative binomial when zeroprob equals \pi_0.

Value

dhnbinom gives the probability mass function, phnbinom gives the distribution function, and rhnbinom generates random deviates.

References

Mullahy, J. (1986) Specification and testing of some modified count data models. Journal of Econometrics, 33, 341-365.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC, doi:10.1201/9780429298547. An older version can be found in https://www.gamlss.com/.

See Also

hnbinom2, hpois, hbinom, zinbinom, ztnbinom

Examples

set.seed(123)
x <- rhnbinom(5, size = 2, prob = 0.4, zeroprob = 0.3)
d <- dhnbinom(x, size = 2, prob = 0.4, zeroprob = 0.3)
p <- phnbinom(x, size = 2, prob = 0.4, zeroprob = 0.3)

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