Count Models Based on Weibull Interarrival Times

In this paper, we introduce a generalized model for count data based upon an assumed Weibull interarrival process that nests the Poisson and negative binomial models as special cases. In addition, we demonstrate that this new Weibull count model can model both over and underdispersed count data, allow covariates to be introduced in a straightforward manner through the hazard function, and be computed in standard software.