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

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  • Hansjörg Albrecher
  • Mogens Bladt
  • Jorge Yslas

Abstract

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.

Suggested Citation

  • Hansjörg Albrecher & Mogens Bladt & Jorge Yslas, 2022. "Fitting inhomogeneous phase‐type distributions to data: the univariate and the multivariate case," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 44-77, March.
    • Handle: RePEc:bla:scjsta:v:49:y:2022:i:1:p:44-77
    DOI: 10.1111/sjos.12505
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    References listed on IDEAS

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    Cited by:

    1. Jamaal Ahmad & Mogens Bladt, 2022. "Phase-type representations of stochastic interest rates with applications to life insurance," Papers 2207.11292, arXiv.org, revised Nov 2022.
    2. Bladt, Martin & Yslas, Jorge, 2023. "Robust claim frequency modeling through phase-type mixture-of-experts regression," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 1-22.
    3. Cheung, Eric C.K. & Peralta, Oscar & Woo, Jae-Kyung, 2022. "Multivariate matrix-exponential affine mixtures and their applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 364-389.
    4. Albrecher, Hansjörg & Bladt, Martin & Bladt, Mogens & Yslas, Jorge, 2022. "Mortality modeling and regression with matrix distributions," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 68-87.
    5. Albrecher Hansjörg & Bladt Martin & Müller Alaric J. A., 2023. "Joint lifetime modeling with matrix distributions," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-22, January.

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