Goodness-of-fit tests for generalized Poisson distributions

TL;DR

This paper introduces computationally efficient goodness-of-fit tests for generalized Poisson distributions, including Compound Poisson and Katz distributions, with demonstrated consistency, bootstrap-based null distribution approximation, and superior or comparable performance in simulations.

Contribution

It develops new goodness-of-fit tests for generalized Poisson distributions that are consistent, computationally convenient, and validated through extensive simulations and real data applications.

Findings

Tests are consistent against fixed alternatives.

Bootstrap method accurately approximates null distribution.

New tests outperform or match existing methods in simulations.

Abstract

This paper presents and examines computationally convenient goodness-of-fit tests for the family of generalized Poisson distributions, which encompasses notable distributions such as the Compound Poisson and the Katz distributions. The tests are consistent against fixed alternatives and their null distribution can be consistently approximated by a parametric bootstrap. The goodness of the bootstrap estimator and the power for finite sample sizes are numerically assessed through an extensive simulation experiment, including comparisons with other tests. In many cases, the novel tests either outperform or match the performance of existing ones. Real data applications are considered for illustrative purposes.