Equi-Under-Dispersed Possion Distribution (EUPoisson)

In this study, we propose an Equi-Under-dispersed Poisson distribution derived from a finite mixture of weighted Poisson distributions. This probability distribution is a simple, parsimonious, and flexible option suitable for modeling under-dispersed count data. It aims to overcome some of the weaknesses of existing methods in modeling Equi-Under-dispersed count data. Explicit expressions for the moment-generating function, mean, variance, and index of dispersion are derived. Real count data are used to compare its performance with that of the zero-inflated Poisson distribution and the finite mixture of Poisson distributions. Maximum likelihood estimation is implemented to estimate the parameters of the distribution, and goodness-of-fit statistical techniques are used to compare the fit of the competing distributions.