RTMBdist (version 1.0.1)

genpois: 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)

Value

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

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.

Examples

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