|
Abstract:
|
In many real-world problems involving extreme events, counts of events often have a heavy-tailed distribution. The Poisson and negative binomial (NB) GLMs are commonly used models for equi- and over-dispersed count data, respectively. A third GLM using the Conway-Maxwell Poisson (COM) distribution has been used to effectively handle under-, over-, and equi-dispersed data sets. However, the three GLMs described above do not typically fit long-tailed data well; the tails of these distributions are still relatively 'light.' In this paper we explore a novel approach for modeling long-tailed distributions using simulated data sets. We then compare the performance of this approach with the Poisson, NB, and COM GLMs. This work provides a stronger basis for selecting a count data regression model, and it provides a new regression model and a comparison of this model with existing approaches.
|
