Models Based on Exponential Interarrival Times for Single-Unusual-Event Count Data

At least one unusual event appears in some count datasets. It will lead to a more concentrated (or dispersed) distribution than the Poisson, the gamma, the Weibull, and the Conway-Maxwell-Poisson (CMP) can accommodate. These well-known count models are based on the equal rates of interarrival times between successive events. Under the assumption of unequal rates (one unusual event) and independent exponential interarrival times, a new class of parametric models for single-unusual-event (SUE) count data is proposed. These two models are applied to two empirical applications, the number of births and the number of bids, and yield considerably better results to the above well-known count models.