Mixed Poisson Regression Models with Varying Dispersion Arising from Non-Conjugate Mixing Distributions

George Tzougas, Natalia Hong, Ryan Ho

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Abstract

In this article we present a class of mixed Poisson regression models with varying dispersion arising from non-conjugate to the Poisson mixing distributions for modelling overdispersed claim counts in non-life insurance. The proposed family of models combined with the adopted modelling framework can provide sufficient flexibility for dealing with different levels of overdispersion. For illustrative purposes, the Poisson-lognormal regression model with regression structures on both its mean and dispersion parameters is employed for modelling claim count data from a motor insurance portfolio. Maximum likelihood estimation is carried out via an expectation-maximization type algorithm, which is developed for the proposed family of models and is demonstrated to perform satisfactorily.

Original languageEnglish
Article number16
JournalAlgorithms
Volume15
Issue number1
Early online date30 Dec 2021
DOIs
Publication statusPublished - Jan 2022

Keywords

  • Claim frequency
  • EM algorithm
  • Non-life insurance
  • Regression structures on the mean and dispersion parameters

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Numerical Analysis
  • Computational Theory and Mathematics
  • Computational Mathematics

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