Smooth Tests for the Zero‐Inflated Poisson Distribution

In this article we construct three smooth goodness‐of‐fit tests for testing for the zero‐inflated Poisson (ZIP) distribution against general smooth alternatives in the sense of Neyman. We apply our tests to a data set previously claimed to be ZIP distributed, and show that the ZIP is not a good model to describe the data. At rejection of the null hypothesis of ZIP, the individual components of the test statistic, which are directly related to interpretable parameters in a smooth model, may be used to gain insight into an alternative distribution.