Maximum Likelihood Estimation in the Truncated, Single Parameter, Discrete Exponential Family

Abstract

A number of papers appear in the literature in which estimates are derived for parameters from truncated discrete probability density functions. A partial list is given in the references. Almost all of these papers deal with either the truncated binomial, negative binomial or poisson cases. These probability density functions are members of the single parameter, discrete exponential family (regular case). In the following, the maximum likelihood estimation equation is derived for all truncated densities which belong to this family. This more general derivation should help unify the work done on maximum likelihood estimation which is scattered throughout the literature.