Inferences for the inflation parameter in the zip distributions: The method of moments

The zero-inflated Poisson (ZIP) distribution is widely used for modeling a count data set when the frequency of zeros is higher than the one expected under the Poisson distribution. There are many methods for making inferences for the inflation parameter in the ZIP models, e.g. the methods for testing Poisson (the inflation parameter is zero) versus ZIP distribution (the inflation parameter is positive). Most of these methods are based on the maximum likelihood estimators which do not have an explicit expression. However, the estimators which are obtained by the method of moments are powerful enough, easy to obtain and implement. In this paper, we propose an approach based on the method of moments for making inferences about the inflation parameter in the ZIP distribution. Our method is also compared to some recent methods via a simulation study and it is illustrated by an example.