On Goodness-of-Fit Tests for the Neyman Type A Distribution

Abstract

The two-parameter Neyman type A distribution is quite useful for modeling count data, since it corresponds to a simple, flexible and overdispersed discrete distribution, which is also zero[1]inflated. In this paper, we show that the probability generating function of the Neyman type A distribution is the only probability generating function which satisfies a certain differential equation. Based on an empirical counterpart of this specific differential equation, we propose and study a new goodness-of-fit test for this distribution. The test is consistent against fixed alternative hypotheses, while its null distribution can be consistently approximated by using parametric bootstrap. We investigate the finite sample performance of the proposed test numerically by means of Monte Carlo experiments, and comparisons with other existing goodness-of-fit tests are also considered. Empirical applications to real data are considered for illustrative purposes.

Keywords

• empirical probability generating function
• parametric bootstrap
• probability generating function
• Bell-Touchard distribution
• count data