EMPIRICAL PROBABILITY GENERATING FUNCTION - AN OVERVIEW

A convenient approach to the statistical analysis of distributions for counts is possible using the empirical probability generating functio n. In this paper we give an overview of recent results and show the us efulness and advantages of this methodology. On one hand, there are so me stochastic models in which the probability generating function aris es naturally and therefore it seems reasonable to use its empirical co unterpart. On the other hand, this statistical tool has demonstrated t o be useful in the study of classical statistical problems of distribu tions for counts, especially in exploratory data analysis, rapid multi -parameter estimation and testing the goodness of fit. Our recommendat ion is to make allowance for the empirical probability generating func tion when dealing with statistical inference for discrete distribution s.