Modeling loss data using mixtures of distributions

Abstract

In this paper, we propose an alternative approach for flexible modeling of heavy tailed, skewed insurance loss data exhibiting multimodality, such as the well-known data set on Danish Fire losses. Our approach is based on finite mixture models of univariate distributions where all K components of the mixture are assumed to be from the same parametric family. Six models are developed with components from parametric,on-Gaussian families of distributions previously used in actuarial modeling: Burr, Gamma, Inverse Burr, Inverse Gaussian, Log-normal, and Weibull. Some of these component distributions are already alone suitable to model data with heavy tails, but do not cover the case of multimodality. Estimation of the models with a fixed number of components K is proposed based on the EM algorithm using three different initialization strategies: distance-based, k-means, and random initialization. Model selection is possible using information criteria, and the fitted models can be used to estimate risk measures for the data, such as VaR and TVaR. The results of the mixture models are compared to the composite Weibull models considered in recent literature as the best models for modeling Danish Fire insurance losses. The results of this paper provide new valuable tools in the area of insurance loss modeling and risk evaluation.