Approximating the poisson probability distribution by the Conway-Maxwell poisson distribution

Abstract

The aim of this research was to approximate the Poisson distribution by the COM-Poisson as a way to induce equi-dispersion in the model and hence, make some inferences by a closedform Poisson distribution. This was done by relating the moments of the COM-Poisson distribution to that of the Poisson distribution to determine the relationship between them. It was found that equi-dispersion could be induced into the count data and hence some inferences on the Neyman-Pearson lemma were made. It was recommended that the COMPoisson distribution should be applied to induce equi-distribution when the data does not conform to the Poisson distribution.