Phase-type distributions for claim severity regression modeling

This paper addresses the task of modeling severity losses using segmentation when the distribution of the data does not fall into the usual regression frameworks. This is not an uncommon situation in lines of business such as third party liability insurance, where heavy-tails and multimodality often hamper a direct statistical analysis. We propose to use regression models based on phase-type distributions, regressing on their underlying inhomogeneous Markov intensity using an extension of the EM algorithm. These models are tailored for survival analysis, but are shown to be well suited for loss data modeling as well. Contrary to the common belief that the distribution of a model is irrelevant if we only wish to estimate the mean, we show that correct segmentation can be obscured or revealed depending on the quality of the baseline distribution.