On the empirical probability generating function based goodness-of-fit tests for count data

Abstract

A convenient way to characterize count data distributions is by their probability generating functions. Therefore, its empirical counterpart, the so-called empirical probability generating function, takes an important place in the construction of goodness-of-fit (GOF) tests. During the talk, we focus on several types of characterizations for discrete data and for each, show general approaches for the construction of GOF test statistics, accompanied by their large sample properties. The methodology is illustrated with several recent examples of GOF tests. A part of the talk is dedicated to the overview of some working results and some potential directions for future research.