Abstract

The Poisson-Garima distribution, the Poisson compound of Garima distribution, was introduced by Shanker to model count data of over dispersed nature and some of the properties along with applications were discussed. It has been observed that some useful statistical properties and reliability properties of the Poisson-Garima distribution was not studied by Shanker. The main purpose of this paper is to discuss the statistical and reliability properties of the Poisson-Garima distribution which was not studied by Shanker and also propose some new applications of the distribution. The proposed distribution is log-concave and a two-component mixture of negative binomial distributions. The hazard function of the distribution has been derived and is increasing and thus the distribution is unimodal. The simulation study has been presented to show the consistency of maximum likelihood estimator of the parameter of Poisson-Garima distribution. It has been shown that the maximum likelihood estimator of the parameter of the distribution is consistent and asymptotically normal. The Poisson-Garima distribution has been applied to four real datasets and found to provide quite satisfactory fit over other competing one parameter over-dispersed count distributions.

Keywords

Poisson-Garima distribution, statistical and reliability properties, simulation, maximum likelihood estimation, goodness of fit