Inference for the Parameters of a Zero-Inflated Poisson Predictive Model

Abstract

In the insurance sector, Zero-Inflated models are commonly used due to the unique nature of insurance data, which often contain both genuine zeros (meaning no claims made) and potential claims. Although active developments in modeling excess zero data have occurred, the use of Bayesian techniques for parameter estimation in Zero-Inflated Poisson models has not been widely explored. This research aims to introduce a new Bayesian approach for estimating the parameters of the Zero-Inflated Poisson model. The method involves employing Gamma and Beta prior distributions to derive closed formulas for Bayes estimators and predictive density. Additionally, we propose a data-driven approach for selecting hyper-parameter values that produce highly accurate Bayes estimates. Simulation studies confirm that, for small and moderate sample sizes, the Bayesian method outperforms the maximum likelihood (ML) method in terms of accuracy. To illustrate the ML and Bayesian methods proposed in the article, a real dataset is analyzed.

Keywords

• bayesian estimation
• ML estimation
• zero-inflated poisson model
• gamma distribution
• beta distribution
• score test