Unusual-event processes for count data

Abstract

At least one unusual event appears in some count datasets. It will lead to a more concentrated (or dispersed) distribution than the Poisson, gamma, Weibull, Conway-Maxwell-Poisson (CMP), and Faddy (1997) models can accommodate. These well-known count models are based on the monotonic rates of interarrival times between successive events. Under the assumption of non-monotonic rates and independent exponential interarrival times, a new class of parametric models for unusual-event (UE) count data is proposed. These 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.