# MultPoisson: Multiplicative Poisson Distribution In rmutil: Utilities for Nonlinear Regression and Repeated Measurements Models

## 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

 ```1 2 3 4``` ```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

`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.
 ```1 2 3 4``` ```dmultpois(5,10,0.9) pmultpois(5,10,0.9) qmultpois(0.85,10,0.9) rmultpois(10,10,0.9) ```