PHASE-TYPE DISTRIBUTIONS FOR CLAIM SEVERITY REGRESSION MODELING

Abstract This paper addresses the task of modeling severity losses using segmentation when data distribution does not fall into usual regression frameworks. situation is uncommon in lines business such as third-party liability insurance, where heavy-tails and multimodality often hamper a direct statistical analysis. We propose to use models based on phase-type distributions, regressing their underlying inhomogeneous Markov intensity an extension expectation–maximization algorithm. These are interpretable tractable terms multistate processes generalize proportional hazards specification dimension state space larger than 1. show that combination matrix parameters, inhomogeneity transforms, covariate information provides flexible effectively capture entire loss severities.