Testing for the generalized Poisson distributions

Abstract

The family of generalized Poisson (GP) distributions, which contain, among many others as special cases, the compound Poisson and Katz distributions, is a flexible family of distributions for modelling count data. The probability generating function (PGF) of the GP is the unique PGF satisfying a certain differential equation. This property leads us to propose and study a goodness-of-fit test for the family of GP distributions. The test is consistent against fixed alternatives, and its 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. Apostolos Batsidis acknowledges support of this work by the project: Establishment of capacity building infrastructures in Biomedical Research (BIOMED-20) (MIS 5047236) which is implemented under the Action Reinforcement of the Research and Innovation Infrastructure, funded by the Operational Programme: Competitiveness, Entrepreneurship and Innovation (NSRF 2014-2020) and co-financed by Greece and the European Union (European Regional Development Fund).