Conwey-Maxwell Poisson Distribution: Approach for Over- and-Under-Dispersed Count Data Modelling

The standard method of count data modeling is Poisson distribution, which has the assumption of equidispersion, as identified by the same mean and variance values. The modelling of count data frequently causes the emergence of over-dispersion which has a higher variance than mean itself. Many research could be found especially for handling over-dispersion problem such Negative Binomial, Zero Inflated Poisson and Quasi approach. However, a few method in research could be fitted under-dispersion problem, such as Generalized Poisson which able to handle both problems, but has limited range of under-dispersion values. In this paper, a review of Conway-Maxwell-Poisson (COM-Poisson) distribution for count data is delivered. The COM-Poisson distribution is not only a generalization of the Poisson distribution, but also the distribution of Bernoulli and Geometric. Furthermore, we compare the performance of Negative Binomial, Generalized Poisson, and COM-Poisson models through its application to real data and simulations on overcome over- and-under-dispersion problem.