R: Multiplicative Poisson Distribution

MultPoisson {rmutil} | R Documentation

## 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(m,s) exp(-m) m^y s^(y^2) / y!

with s <= 1 for y = 0, …, 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(s)

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)

[Package rmutil version 1.1.3 Index]