R: Poisson-Gamma Distribution (Negative-Binomial)

pg.dist

R Documentation

Poisson-Gamma Distribution (Negative-Binomial)

Description

The function fits a mixed Poisson distribution, in which the random parameter follows Gamma distribution (the negative-binomial distribution). As teh method of estimation Expectation-maximization algorithm is used. In M-step the analytical formulas taken from [Karlis, 2005] are applied.

Usage

pg.dist(variable, alpha.start, beta.start, epsylon)

Arguments

`variable`	The count variable.
`alpha.start`	The starting value of the parameter alpha. Default to 1.
`beta.start`	The starting value of the parameter beta. Default to 0.3
`epsylon`	Default to epsylon = 10^(-8)

Details

This function provides estimated parameters of the model N|λ \sim Poisson(λ) where λ parameter is also a random variable follows Gamma distribution with hiperparameters α, β. The pdf of Gamma is of the form f_λ(λ)=\frac{λ^{α-1}\exp(-βλ)β^λ}{Γ(α)} .

Value

`alpha`	the parameter of mixing Gamma distribution
`beta`	the parameter of mixing Gamma distribution
`theta`	the value 1/beta
`n.iter`	the number of steps in EM algorithm

References

Karlis, D. (2005). EM algorithm for mixed Poisson and other discrete distributions. Astin bulletin, 35(01), 3-24.

Examples

library(MASS)
pGamma1 = pg.dist(variable=quine$Days)
print(pGamma1)