Zero-inflated Poisson-Akash distribution for count data with excessive zeros

Abstract

Over-dispersed models are often used whenever the variation is more than what in point of fact is anticipated by a model. One of the reasons behind experiencing over-dispersion is an excessive number of zeros, hence when modeling this observed fact, we use zero-inflated models rather than more traditional ones. As a part of our research, we have suggested a zero-inflated variant of Poisson-Akash distribution that was introduced in 2015. We have calculated crucial statistical characteristics of the suggested model which are not confined to generating functions, over-dispersion property, moments and associated measures. The parametric estimation has been carried out using the maximum likelihood estimation. Two different simulation exercises have been carried out, one to test the performance of maximum likelihood estimates and the other for testing the compatibility of our devised model when data has been simulated from different zero-inflated models. For the purpose of testing the compatibility of our proposed model, we have used four real life data sets and considered different performance measures like Goodness-of-fit, Akaike’s information criterion, Bayesian information criterion, Dispersion index etc. The fitting results have been compared with some other models of interest. Moreover, we have tested the significance of the zero-inflation parameter using Likelihood ratio test, Score test and the Wald test itself.