A Model Selection Criterion for Count Models Based on a Divergence Between Probability Generating Functions

Abstract

AbstractModel selection criteria are often used to choose the best fitting distribution among a set of candidate models for describing the data. Plethora of model selection criteria have been developed over the years by constructing estimators of discrepancy measures that assess the divergence between the true model and a fitted approximating model in terms of their probability mass functions or probability density functions. This contribution focuses on a model selection criterion for count models, which assess the divergence between the true model and a fitted approximating model in terms of probability generating functions. The proposed model selection criterion is appealing in cases where the likelihood of a model is not regular enough. An example is presented where the proposed model selection criterion can be applied, while ordinary ones, such as the Akaike Information Criterion, cannot. Finally, the performance of the proposed model selection criterion is evaluated and compared with the respective of the Akaike Information Criterion based on a Monte Carlo study in a case where both approaches can be applied.