rmutil (version 1.1.10)

MultPoisson: Multiplicative Poisson Distribution

Description

These functions provide information about the multiplicative Poisson distribution with parameters m and s: density, cumulative distribution, quantiles, and random generation.

The multiplicative Poisson distribution with mu \(= m\) has density $$p(y) = c({\mu}, {\lambda})\exp({-\mu}) {\mu}^{y} {\lambda}^({y}^2) / {y!}% $$ with \(s <= 1\) for \(y = 0, \ldots\), where c(.) is a normalizing constant.

Note that it only allows for underdispersion, not being defined for \(s > 1\).

Usage

dmultpois(y, m, s, log=FALSE)
pmultpois(q, m, s)
qmultpois(p, m, s)
rmultpois(n, m, s)

Arguments

y

vector of counts

q

vector of quantiles

p

vector of probabilities

n

number of values to generate

m

scalar or vector of means

s

scalar or vector of overdispersion parameters, all of which must lie in (0,1).

log

if TRUE, log probabilities are supplied.

Author

J.K. Lindsey

See Also

dpois for the Poisson, ddoublepois for the double Poisson, dpvfpois for the power variance function Poisson, dconsul for the Consul generalized Poisson, dgammacount for the gamma count, and dnbinom for the negative binomial distribution.

Examples

dmultpois(5,10,0.9)
pmultpois(5,10,0.9)
qmultpois(0.85,10,0.9)
rmultpois(10,10,0.9)