Claims Modelling with Three-Component Composite Models

In this paper, we develop a number of new composite models for modelling individual claims in general insurance. All our models contain a Weibull distribution for the smallest claims, a lognormal distribution for the medium-sized claims, and a long-tailed distribution for the largest claims. They provide a more detailed categorisation of claims sizes when compared to the existing composite models which differentiate only between the small and large claims. For each proposed model, we express four of the parameters as functions of the other parameters. We fit these models to two real-world insurance data sets using both maximum likelihood and Bayesian estimation, and test their goodness-of-fit based on several statistical criteria. They generally outperform the existing composite models in the literature, which comprise only two components. We also perform regression using the proposed models.