Tests and Confidence Intervals for the Mean of a Zero-Inflated Poisson Distribution

Abstract The zero-inflated Poisson (ZIP) model is often postulated for count data that include excessive zeros. This ZIP distribution can be regarded as the mixture of two distributions, one that degenerate at zero and another is Poisson. Unlike the Poisson mean, the mean of the ZIP distribution is product of the mixture parameter and the Poisson parameter, and is not simple to make inference on the ZIP mean. In this article, the problem of making inference on the mean of a ZIP distribution is addressed. Confidence intervals based on the likelihood approach and bootstrap approach are provided. Signed likelihood ratio test for one-sided hypothesis is also developed. Proposed methods are evaluated for their properties by Monte Carlo simulation. Methods are illustrated using two examples.