Abstract

The Poisson-Suja distribution, the Poisson compound of Suja distribution, was introduced to model count data of over-dispersed nature from biological sciences. The main purpose of this paper is to derive some statistical and reliability properties of Poisson-Suja distribution which have not been studied earlier. It has been observed that the proposed distribution is log-concave and is a two-component mixture of negative binomial distributions. The cumulative distribution function, survival function and hazard function of the Poisson-Suja distribution have been derived and their natures for varying values of parameter have been presented. The expressions for other reliability parameter including reverse hazard rate function, the second rate of failure, the cumulative hazard function and the Mills ratio of the Poisson-Suja distribution have also been derived. The simulation study has been presented to show the consistency of maximum likelihood estimator of the parameter of Poisson-Suja distribution. The Poisson-Suja distribution has been applied to two real datasets and found to provide quite satisfactory fit over other competing one parameter over-dispersed count distributions namely Poisson-Lindley distribution, Poisson-Komal distribution, PoissonShanker distribution, and Poisson-Garima distribution.

Keywords

suja distribution, poisson-suja distribution, statistical properties, reliability properties, estimation of parameter, simulation, applications