A count data model for gamma waiting times

Abstract

A new distribution for non-negative integers, or counts, is developed. It is based on the assumption that the waiting times separating consecutive events are independently and identically gamma distributed. Thus, the structural process generating the counts may exhibit duration dependence. In this framework, the frequently observed phenomenon of overdispersion, that is a variance that exceeds the mean, is caused by a decreasing hazard function of the gamma distributed waiting times, while an increasing hazard leads to underdispersion at the level of the counts. A Monte Carlo simulation and an application to fertility data illustrate the performance of the new distribution.