A Counting Process with Generalized Exponential Inter-Arrival Times

Abstract

This paper introduces a new counting process which is based on Generalized Exponentially distributed inter-arrival times. The advantage of this new count model over the existing Poisson count model is that the hazard function of the inter arrival time distribution is non-constant, so that the distribution is duration dependent and hence, is able to model both under dispersed and over dispersed count data, as opposed to the exponentially distributed inter arrival time of the Poisson count model, which is not duration dependent and the corresponding count model is able to model only equidispersed data. Further, some properties of this model are explored. Simulation from this new model is performed to study the behavior of count probabilities, mean and variance of the model for different values of the parameter. Use of the proposed model is illustrated with the help of real life data sets on arrival times of patients at a clinic and on arrival times of customers at a departmental store.