Fitting inhomogeneous phase-type distributions to data: the univariate and the multivariate case [article]

Hansjoerg Albrecher, Mogens Bladt, Jorge Yslas
2020 arXiv   pre-print
The class of inhomogeneous phase-type distributions (IPH) was recently introduced in Albrecher and Bladt (2019) as an extension of the classical phase-type (PH) distributions. Like PH distributions, the class of IPH is dense in the class of distributions on the positive halfline, but leads to more parsimonious models in the presence of heavy tails. In this paper we propose a fitting procedure for this class to given data. We furthermore consider an analogous extension of Kulkarni's multivariate
more » ... phase-type class (Kulkarni, 1989) to the inhomogeneous framework and study parameter estimation for the resulting new and flexible class of multivariate distributions. As a by-product, we amend a previously suggested fitting procedure for the homogeneous multivariate phase-type case and provide appropriate adaptations for censored data. The performance of the algorithms is illustrated in several numerical examples, both for simulated and real-life insurance data.
arXiv:2006.13003v2 fatcat:haw2wfkrwfaejm2pmuglgcwi7q