Estimating parameters for discrete distributions via the empirical probability generating function

Abstract

We consider parameter estimation for a family of discrete distributions characterized by probability generating functions (pgf's). Kemp and Kemp (1988) suggest estimators based on the empirical probability generating function (epgf) the methods involve solving estimating equations obtained by equating functionals of the epgf and pgf on a fixed, finite set of values. We derive asymptotic theory for these estimators and consider some examples. Graphical techniques based on the theory are shown to be useful for exploratory analysis