ON KEMPTON’S GENERALIZATION OF THE NEGATIVE BINOMIAL DISTRIBUTION

Abstract

This paper examines the properties, applications to empirical modelling and computation of probabilities of Kempton’s generalization of the negative binomial and log-series distributions. The 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. Although 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.