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A note on the connection between some classical mortality laws and proportional frailty

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  • Lindholm, Mathias

Abstract

We provide a simple frailty argument that produces the Gompertz–Makeham mortality law as the population hazard rate under the assumption of proportional frailty given a common exponential hazard rate. Further, based on a slight generalisation of the result for the Gompertz–Makeham law the connection to Perks and Beard’s mortality laws is discussed. Moreover, we give conditions for which functional forms of the baseline hazard that will yield proper frailty distributions given we want to retrieve a certain overall population hazard within the proportional frailty framework.

Suggested Citation

  • Lindholm, Mathias, 2017. "A note on the connection between some classical mortality laws and proportional frailty," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 76-82.
    • Handle: RePEc:eee:stapro:v:126:y:2017:i:c:p:76-82
    DOI: 10.1016/j.spl.2017.02.013
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    1. Butt, Zoltan & Haberman, Steven, 2004. "Application of Frailty-Based Mortality Models Using Generalized Linear Models," ASTIN Bulletin, Cambridge University Press, vol. 34(1), pages 175-197, May.
    2. Trifon I. Missov & Maxim S. Finkelstein, 2011. "Admissible mixing distributions for a general class of mixture survival models with known asymptotics," MPIDR Working Papers WP-2011-004, Max Planck Institute for Demographic Research, Rostock, Germany.
    3. Trifon Missov & Adam Lenart & Laszlo Nemeth & Vladimir Canudas-Romo & James W. Vaupel, 2015. "The Gompertz force of mortality in terms of the modal age at death," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 32(36), pages 1031-1048.
    4. Missov, Trifon I. & Finkelstein, Maxim, 2011. "Admissible mixing distributions for a general class of mixture survival models with known asymptotics," Theoretical Population Biology, Elsevier, vol. 80(1), pages 64-70.
    5. James W. Vaupel & Trifon Missov, 2014. "Unobserved population heterogeneity," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 31(22), pages 659-686.
    6. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
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