Inhomogeneous phase-type distributions and heavy tails. (December 2019)

• Record Type: Journal Article
• Authors: Albrecher, Hansjörg; Bladt, Mogens
• Is Part Of: Journal of applied probability. Volume 56:Number 4(2019)
• Page Start: 1044
• Page End: 1064
• Publication Date: 2019-12
• Subjects: Inhomogeneous phase-type, -- heavy tail, -- product integral, -- matrix Pareto distribution, -- matrix Weibull distribution; Primary 60J27, -- Secondary 62F10, -- 62M05; 519.2
• DOI: 10.1017/jpr.2019.60
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract: We extend the construction principle of phase-type (PH) distributions to allow for inhomogeneous transition rates and show that this naturally leads to direct probabilistic descriptions of certain transformations of PH distributions. In particular, the resulting matrix distributions enable the carrying over of fitting properties of PH distributions to distributions with heavy tails, providing a general modelling framework for heavy-tail phenomena. We also illustrate the versatility and parsimony of the proposed approach in modelling a real-world heavy-tailed fire insurance dataset.