A reconsideration of the Pólya-Aeppli model

Abstract

A reconsideration of the Pólya-Aeppli distribution, usually denoted by PAD, is made with the intent of focusing its role as a model for count data analysis. To this aim, an infinite matrix of numbers based on simple recurrence formulas is given for computing the probabilities without difficulty. Hence , it is pointed out how the parameterisation used facilitates also the ML- estimation. Then, an extension of usual parametric space allowing the PAD to be regarded as both an under- and over – dispersion model is considered. Examples are given for elucidating the utility of PAD also in comparison with models used to analyse overdispersion in a broader sense.