
Statistics Papers
Document Type
Technical Report
Date of this Version
2008
Publication Source
Journal of Business & Economic Statistics
Volume
26
Issue
3
Start Page
369
Last Page
378
DOI
10.1198/073500107000000278
Abstract
The widespread popularity and use of both the Poisson and the negative binomial models for count data arise, in part, from their derivation as the number of arrivals in a given time period assuming exponentially distributed interarrival times (without and with heterogeneity in the underlying base rates, respectively). However, with that clean theory come some limitations including limited flexibility in the assumed underlying arrival rate distribution and the inability to model underdispersed counts (variance less than the mean). Although extant research has addressed some of these issues, there still remain numerous valuable extensions. In this research, we present a model that, due to computational tractability, was previously thought to be infeasible. In particular, we introduce here a generalized model for count data based upon an assumed Weibull interarrival process that nests the Poisson and negative binomial models as special cases. The computational intractability is overcome by deriving the Weibull count model using a polynomial expansion which then allows for closed-form inference (integration term-by-term) when incorporating heterogeneity due to the conjugacy of the expansion and a commonly employed gamma distribution. In addition, we demonstrate that this new Weibull count model can (1) model both over- and underdispersed count data, (2) allow covariates to be introduced in a straightforward manner through the hazard function, and (3) be computed in standard software.
Copyright/Permission Statement
This is an Accepted Manuscript of an article published by Taylor & Francis in the Journal of Business & Economics Statistics in 2008, available online: http://dx.doi.org/10.1198/073500107000000278
Keywords
closed-form inferences, hazard models, polynomial expressions
Recommended Citation
McShane, B., Adrian, M., Bradlow, E. T., & Fader, P. S. (2008). Count Models Based on Weibull Interarrival Times. Journal of Business & Economic Statistics, 26 (3), 369-378. http://dx.doi.org/10.1198/073500107000000278
Date Posted: 25 October 2018
This document has been peer reviewed.