gp.mle {gp}

Maximum likelihood estimation of the generalized Poisson distribution

Description

Maximum likelihood estimation of the generalized Poisson distribution.

Usage

gp.mle(y)

Arguments

y

A vector with non negative integer values.

Details

The probability density function of the generalized Poisson distribution is the following (Nikoloulopoulos & Karlis, 2008):

P(Y=y|\theta, \lambda)=\theta(\theta+\lambda y)^{y-1}\frac{e^{-\theta-\lambda y}}{y!}, \ \ y=0,1... \ \ \theta >0, \ \ 0 \leq \lambda \leq 1.

To ensure that \theta is positive we use the "log" link and for \lambda to lie within 0 and 1 we use the "logit" link within the optim function.

Value

A vector with three numbers, the \theta and \lambda parameters and the value of the log-likelihood.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

References

Nikoloulopoulos A.K. & Karlis D. (2008). On modeling count data: a comparison of some well-known discrete distributions. Journal of Statistical Computation and Simulation, 78(3): 437–457.

See Also

gp.reg, rgp

Examples

y <-  rgp(1000, 10, 0.5, method = "Inversion")
gp.mle(y)