## 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

 1 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

 1 2 3 library(MASS) pLindley = pl.dist(variable=quine\$Days) print(pLindley) 

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