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An Empirical Assessment of Over-Dispersion in Zero Inflated Poisson and Conway-Maxwell Poisson Probability Distributions
Keywords
Equi-dispersion,Power series distribution, Zero inflation, COM-Poisson, ZI-Poisson
Abstract
A zero inflated probability model arises when probability mass at point zero exceeds the one allowed under the standard parametric family of discrete distribution. Ignoring zero inflation can as a consequence, result in biasedness in the estimated parameters and standard errors as well as causing over-dispersion when fitting a discrete generalized linear model. In the case of a Poisson distribution, the equi-dispersion property no longer holds rendering the model not suitable for analysis. Variants of the Poisson distribution model have been proposed and studied. Among these are the Conway-Maxwell Poisson (COM-Poisson) and the Zero-inflated Poisson (ZI-Poisson). In this paper, we empirically evaluate the equi-dispersion property when the two models are fitted to some data. It is observed that whereas the parameter transformed COM-Poisson model (Arua and Sakia, 2015) induced a near- perfect equi-dispersion to the data, the Zero inflated model still exhibited some over-dispersion despite a substantial reduction of the zero inflation factor.