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Joint lifetime modeling with matrix distributions

Author

Listed:
  • Albrecher Hansjörg

    (Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny, 1015 Lausanne, Switzerland)

  • Bladt Martin

    (Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny, 1015 Lausanne, Switzerland)

  • Müller Alaric J. A.

    (Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny, 1015 Lausanne, Switzerland)

Abstract

Acyclic phase-type (PH) distributions have been a popular tool in survival analysis, thanks to their natural interpretation in terms of aging toward its inevitable absorption. In this article, we consider an extension to the bivariate setting for the modeling of joint lifetimes. In contrast to previous models in the literature that were based on a separate estimation of the marginal behavior and the dependence structure through a copula, we propose a new time-inhomogeneous version of a multivariate PH (mIPH) class that leads to a model for joint lifetimes without that separation. We study properties of mIPH class members and provide an adapted estimation procedure that allows for right-censoring and covariate information. We show that initial distribution vectors in our construction can be tailored to reflect the dependence of the random variables and use multinomial regression to determine the influence of covariates on starting probabilities. Moreover, we highlight the flexibility and parsimony, in terms of needed phases, introduced by the time inhomogeneity. Numerical illustrations are given for the data set of joint lifetimes of Frees et al., where 10 phases turn out to be sufficient for a reasonable fitting performance. As a by-product, the proposed approach enables a natural causal interpretation of the association in the aging mechanism of joint lifetimes that goes beyond a statistical fit.

Suggested Citation

  • 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.
    • Handle: RePEc:vrs:demode:v:11:y:2023:i:1:p:22:n:1
    DOI: 10.1515/demo-2022-0153
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    References listed on IDEAS

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    1. Spreeuw, Jaap & Owadally, Iqbal, 2013. "Investigating the Broken-Heart Effect: a Model for Short-Term Dependence between the Remaining Lifetimes of Joint Lives," Annals of Actuarial Science, Cambridge University Press, vol. 7(2), pages 236-257, September.
    2. Søren Asmussen & Patrick J. Laub & Hailiang Yang, 2019. "Phase-Type Models in Life Insurance: Fitting and Valuation of Equity-Linked Benefits," Risks, MDPI, vol. 7(1), pages 1-22, February.
    3. Luciano, Elisa & Spreeuw, Jaap & Vigna, Elena, 2008. "Modelling stochastic mortality for dependent lives," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 234-244, October.
    4. X. Lin & Xiaoming Liu, 2007. "Markov Aging Process and Phase-Type Law of Mortality," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(4), pages 92-109.
    5. Khouzeima Moutanabbir & Hassan Abdelrahman, 2022. "Bivariate Sarmanov Phase-Type Distributions for Joint Lifetimes Modeling," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1093-1118, June.
    6. 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.
    7. Min Ji & Mary Hardy & Johnny Siu-Hang Li, 2011. "Markovian Approaches to Joint-Life Mortality," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(3), pages 357-376.
    8. 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.
    9. Gobbi, Fabio & Kolev, Nikolai & Mulinacci, Sabrina, 2019. "Joint Life Insurance Pricing Using Extended Marshall–Olkin Models," ASTIN Bulletin, Cambridge University Press, vol. 49(2), pages 409-432, May.
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