A flexible and computationally tractable discrete distribution derived from a stationary renewal process

Abstract

A class of discrete distributions can be derived from stationary renewal processes. They have the useful property that the mean is a simple function of the model parameters. Thus regressions of the distribution mean on covariates can be carried out and marginal effects of covariates calculated. Probabilities can be easily computed in closed form for only two such distributions, when the event interarrival times in the renewal process follow either a gamma or an inverse Gaussian distribution. The gamma-based distribution has more attractive properties and is described and fitted to data. The inverse-Gaussian based distribution is also briefly discussed.