Poisson-Lindley Distribution

Description

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

Usage

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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|λ \sim Poisson(λ) where λ parameter is also a random variable follows Lindley distribution with hiperparameter p. The pdf of Lindley is of the form f_λ(λ)=\frac{p^2}{p+1}(λ+1)\exp(-λ 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

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