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Approximating the Poisson Probability Distribution by the Conway-Maxwell Poisson Distribution
Keywords
Poisson distribution, COM-Poisson distribution, equi-dispersion
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 taking advantage of the close-form moments of the Poisson distribution. This was achieved by relating the approximate moments of the COM-Poisson distribution to that of the Poisson distribution to determine the relationship between their respective parameters. The estimates of the Poisson parameters were found to induce equi-distribution to the observed data. The advantage of the estimation is that closed-form moments of the Poisson can then be used to make inferences on the data. It is recommended that the COM-Poisson distribution should be applied to induce equi-distribution when the data does not conform to the Poisson distribution.