Choice of mixture Poisson models based on Extreme value theory

TL;DR

This paper introduces a novel method using extreme value theory to select the best mixture Poisson model among Fréchet, Gumbel, and pseudo-Gumbel distributions, improving count data modeling especially with overdispersion.

Contribution

It proposes an original decision tree-based strategy to identify the most suitable mixing distribution for mixture Poisson models using extreme value theory.

Findings

Effective decision tree approach for model selection

Numerical simulations validate the strategy's accuracy

Improved modeling of overdispersed count data

Abstract

Count data are omnipresent in many applied fields, often with overdispersion due to an excess of zeroes or extreme values. With mixtures of Poisson distributions representing an elegant and appealing modelling strategy, we focus here on the challenging problem of identifying a suitable mixing distribution and study how extreme value theory can be used. We propose an original strategy to select the most appropriate candidate among three categories: Fr{\'e}chet, Gumbel and pseudo-Gumbel. Such an approach is presented with the aid of a decision tree and evaluated with numerical simulations.