pl.dist {MixedPoisson}

Poisson-Lindley Distribution

Description

The function fits a mixed Poisson distribution, in which the random parameter follows Lindley distribution. As teh method of estimation Expectation-maximization algorithm is used.

Usage

pl.dist(variable, p.start, epsylon)

Arguments

variable

The count variable.

p.start

The starting value of p parameter. Default to 0.1.

epsylon

Default to epsylon = 10^(-8)

Details

This function provides estimated parameters of the model N|\lambda \sim Poisson(\lambda) where \lambda parameter is also a random variable follows Lindley distribution with hiperparameter p. The pdf of Lindley is of the form f_\lambda(\lambda)=\frac{p^2}{p+1}(\lambda+1)\exp(-\lambda p) .

Value

p

the parameter of mixing Lindley distribution

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)
pLindley = pl.dist(variable=quine$Days)
print(pLindley)