gp.mle: Maximum likelihood estimation of the generalized Poisson distribution
Description
Maximum likelihood estimation of the generalized Poisson distribution.
Usage
gp.mle(y)
Value
A vector with three numbers, the \(\theta\) and \(\lambda\) parameters and the value of the log-likelihood.
Arguments
y
A vector with non negative integer values.
Author
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
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.
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.