On characterization and goodness-of-fit test of some discrete distribution families

In this article a non-negative integer-valued random variable which is distributed according to a power-series distribution law, is characterized as Poisson, binomial, or negative binomial by relating its first- and second-order moments. In addition, we show that the characterizations can be used to derive goodness-of-fit tests for Poisson, binomial, and negative binomial families. The resulting tests are closely related to those based on Fisher's index of dispersion. Their performances compared with the classical Pearson-Fisher chi-squared tests are investigated in a Monte Carlo study. (C) 1998 Elsevier Science B.V. All rights reserved.