genpois: Generalised Poisson distribution

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

Generalised Poisson distribution

Description

Probability mass function, distribution function, and random generation for the generalised Poisson distribution.

Usage

dgenpois(x, lambda = 1, phi = 1, log = FALSE)

pgenpois(q, lambda = 1, phi = 1, lower.tail = TRUE, log.p = FALSE)

qgenpois(p, lambda = 1, phi = 1,
         lower.tail = TRUE, log.p = FALSE, max.value = 10000)

rgenpois(n, lambda = 1, phi = 1, max.value = 10000)

Arguments

x, q	integer vector of counts
lambda	vector of positive means
phi	vector of non-negative dispersion parameters
log, log.p	logical; return log-density if TRUE
lower.tail	logical; if TRUE, probabilities are P[X \le x], otherwise, P[X > x].
p	vector of probabilities
max.value	a constant, set to the default value of 10000 for how far the algorithm should look for q.
n	number of random values to return.

Details

This implementation of dgenpois allows for automatic differentiation with RTMB. The other functions are imported from gamlss.dist::GPO.

The distribution has mean \lambda and variance \lambda(1 + \phi \lambda)^2. For \phi = 0 it reduces to the Poisson distribution, however \phi must be strictly positive here.

Value

dgenpois gives the probability mass function, pgenpois gives the distribution function, qgenpois gives the quantile function, and rgenpois generates random deviates.

Examples

set.seed(123)
x <- rgenpois(1, 2, 3)
d <- dgenpois(x, 2, 3)
p <- pgenpois(x, 2, 3)
q <- qgenpois(p, 2, 3)

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