TY - JOUR

T1 - Fitting inhomogeneous phase-type distributions to data

T2 - the univariate and the multivariate case

AU - Albrecher, Hansjörg

AU - Bladt, Mogens

AU - Yslas, Jorge

PY - 2022

Y1 - 2022

N2 - The class of inhomogeneous phase-type distributions (IPH) was recently introduced in Albrecher & 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 PH 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 PH 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.

AB - The class of inhomogeneous phase-type distributions (IPH) was recently introduced in Albrecher & 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 PH 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 PH 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.

KW - heavy tails

KW - inhomogeneous phase-type

KW - matrix Pareto distribution

KW - matrix Weibull distribution

KW - multivariate phase-type

KW - parameter estimation

UR - http://www.scopus.com/inward/record.url?scp=85098326659&partnerID=8YFLogxK

U2 - 10.1111/sjos.12505

DO - 10.1111/sjos.12505

M3 - Journal article

AN - SCOPUS:85098326659

VL - 49

SP - 44

EP - 77

JO - Scandinavian Journal of Statistics

JF - Scandinavian Journal of Statistics

SN - 0303-6898

IS - 1

ER -