On Kempton's Generalization of the Negative Binomial Distribution

This paper examines the properties of and applications to empirical modelling as well as computation of probabilities of Kempton's generalization of the negative binomial and log-series distributions. Important properties of infinite divisibility and unimodality have been derived. To facilitate computation of the complicated probabilities, practical implementation of the three-term probability recurrence relations is presented. While the generalization of the negative binomial and log-series distributions have been formulated to fit extremely long-tailed count data, the versatility of this generalized negative binomial distribution to fit short-tailed and long-tailed data is illustrated here.