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The class of inhomogeneous phase-type distributions (IPH) was recentlyintroduced in Albrecher and Bladt (2019) as an extension of the classicalphase-type (PH) distributions. Like PH distributions, the class of IPH is densein the class of distributions on the positive halfline, but leads to moreparsimonious models in the presence of heavy tails. In this paper we propose afitting procedure for this class to given data. We furthermore consider ananalogous extension of Kulkarni's multivariate phase-type class (Kulkarni,1989) to the inhomogeneous framework and study parameter estimation for theresulting new and flexible class of multivariate distributions. As aby-product, we amend a previously suggested fitting procedure for thehomogeneous multivariate phase-type case and provide appropriate adaptationsfor censored data. The performance of the algorithms is illustrated in severalnumerical examples, both for simulated and real-life insurance data.

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