Testing for the Poisson–Tweedie distribution

Abstract In practice, count data exhibit over-dispersion, zero-inflation and even heavy tails. The Poisson–Tweedie distribution is a flexible parametric family able to accommodate these features. This paper proposes and studies a computationally convenient goodness-of-fit test for this distribution, which is based on an empirical counterpart of a system of equations. The test is consistent against fixed alternatives. The null distribution of the test can be consistently approximated by a parametric bootstrap. The goodness of the bootstrap estimator and the power for finite sample sizes are numerically assessed. Comparisons with other tests are also included. Applications to two real data sets are displayed.