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

TL;DR

This paper introduces a new class of count models based on unequal exponential interarrival times to better handle datasets with at least one unusual event, outperforming traditional models like Poisson and CMP.

Contribution

It proposes a novel parametric modeling approach for single-unusual-event count data using unequal exponential interarrival times, filling a gap in existing models.

Findings

Models outperform traditional Poisson and CMP in empirical applications.

Better fit for datasets with at least one unusual event.

Applicable to diverse count data like births and bids.

Abstract

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.