pg.dist: Poisson-Gamma Distribution (Negative-Binomial)
In MixedPoisson: Mixed Poisson Models

Description Usage Arguments Details Value References Examples

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.

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

`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)

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)} .

`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

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

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

Loading required package: gaussquad
Loading required package: polynom
Loading required package: orthopolynom
Loading required package: Rmpfr
Loading required package: gmp

Attaching package: 'gmp'

The following objects are masked from 'package:base':

    %*%, apply, crossprod, matrix, tcrossprod

C code of R package 'Rmpfr': GMP using 64 bits per limb


Attaching package: 'Rmpfr'

The following objects are masked from 'package:stats':

    dbinom, dnorm, dpois, pnorm

The following objects are masked from 'package:base':

    cbind, pmax, pmin, rbind

Loading required package: MASS
$alpha
[1] 15.73654

$beta
[1] 0.9561112

$theta
[1] 1.045903

$n.iter
[1] 66

attr(,"class")
[1] "pg.dist"