ABSTRACT This article proposes three new goodness‐of‐fit tests for the zero‐altered Poisson distribution, or equivalently for the positive Poisson distribution, based on positive data, that is, data truncated at 0, whose test statistic is built using a characterization of this law. It is shown that the proposed tests are consistent against any fixed alternative and that the parametric bootstrap method can accurately approximate their null distributions. The power of these tests is investigated through a large simulation study, where it is also compared with some existing tests, showing a very competitive behavior. Several applications to real datasets illustrate the usefulness of the tests.
Jiménez–Gamero et al. (2025) studied this question.