A New Generalization of Poisson Distribution for Over-dispersed, Count Data: Mathematical Properties, Regression Model and Applications

In this article, the discrete distribution named Poisson distribution was compounded with a continuous distribution, i.e., NXLindley distribution to generate the Poisson–NXLindley distribution. Its basic mathematical properties were explored and a general expression for its ordinary factorial moments, moment generating function, dispersion index, coefficient of variation, skewness, and kurtosis. The proposed distribution is over-dispersed since its mean is less than the variance. This feature opens a new opportunity to model over-dispersed count datasets. The maximum likelihood approach is used for the estimation of the unknown parameter of the proposed model. Three real-life datasets are used to show the applicability of the new distribution. Additionally, the count regression model based on the Poisson–NXLindley distribution is introduced. The new model efficiently analyzed considered datasets than the competitive one-parameter discrete distribution.