Parametric Inference on Zero-Inflated Poisson distribution
and its variants

Santanu Chakraborty
Mathematics Department
UT Pan-American

Abstract

            The zero-inflated Poisson distribution has found enough study importance in the recent years for modeling count data, some biologoical phenomena and also in software developments in computer science. This distribution is derived from a usual Poisson probability distribution using a very simple-minded approach. Starting with a Poisson random variable with parameter $\lambda$, one can construct a Zero-Inflated Poisson (ZIP) variable by reducing the mass at each of the non-zero values by a constant proportion and increasing the mass at zero accordingly. This was the original definition of a Zero-Inflated Poisson random variable. Later there have been several generalizations of ZIP.

            In this talk, we shall study some estimation and testing procedures for the Zero-inflated Poisson parameters and some of the interesting variants of ZIP. In particular, we demonstrate how to get rid of the nuisance parameters by conditioning on sufficient statistics.