Three Classes of Univariate Discrete Distributions

Abstract

Families of descrete distributions have been developed and studied by many authors, including, Neyman [1939], Feller [1943], Skellam [1952], Beall and Rescia [1953] and Gurland [1957, 1958]. These families are of three types: Type A: gA(z) = exp {h(z)}, Type B: gB(Z) = {h(z) 1', Type C: gc(z) = c log {h(z)}, where g(z) represents a probability generating function (p.g.f.) and h(z) is a p.g.f., except possibly for additive and multiplicative constants. The aim of this paper is to set up formulae for certain statistics for these types. It is hoped that these will be of use to reseach workers in practical fields, who will be formulating compound and generalised distributions of these types by using specific forms of h(z).