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Justifying the Gompertz curve of mortality via the generalized Polya process of shocks

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  • Cha, Ji Hwan
  • Finkelstein, Maxim

Abstract

A new probabilistic model of aging that can be applied to organisms is suggested and analyzed. Organisms are subject to shocks that follow the generalized Polya process (GPP), which has been recently introduced and characterized in the literature. Distinct from the nonhomogeneous Poisson process that has been widely used in applications, the important feature of this process is the dependence of its future behavior on the number of previous events (shocks). The corresponding survival and the mortality rate functions are derived and analyzed. The general approach is used for justification of the Gompertz law of human mortality.

Suggested Citation

  • Cha, Ji Hwan & Finkelstein, Maxim, 2016. "Justifying the Gompertz curve of mortality via the generalized Polya process of shocks," Theoretical Population Biology, Elsevier, vol. 109(C), pages 54-62.
    • Handle: RePEc:eee:thpobi:v:109:y:2016:i:c:p:54-62
    DOI: 10.1016/j.tpb.2016.03.001
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    References listed on IDEAS

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    1. Toshio Nakagawa, 2007. "Shock and Damage Models in Reliability Theory," Springer Series in Reliability Engineering, Springer, number 978-1-84628-442-7, December.
    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. Maxim Finkelstein, 2012. "Discussing the Strehler-Mildvan model of mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 26(9), pages 191-206.
    4. Finkelstein, Maxim, 2012. "On ordered subpopulations and population mortality at advanced ages," Theoretical Population Biology, Elsevier, vol. 81(4), pages 292-299.
    5. 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.
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    7. Y. Kebir, 1991. "On hazard rate processes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(6), pages 865-876, December.
    8. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, December.
    9. David Steinsaltz & Kenneth Wachter, 2006. "Understanding Mortality Rate Deceleration and Heterogeneity," Mathematical Population Studies, Taylor & Francis Journals, vol. 13(1), pages 19-37.
    10. Asfaw, Zeytu Gashaw & Lindqvist, Bo Henry, 2015. "Extending minimal repair models for repairable systems: A comparison of dynamic and heterogeneous extensions of a nonhomogeneous Poisson process," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 53-58.
    11. Maxim Finkelstein & Ji Hwan Cha, 2013. "Burn-in for Heterogeneous Populations," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 261-312, Springer.
    12. Li, Ting & Anderson, James J., 2009. "The vitality model: A way to understand population survival and demographic heterogeneity," Theoretical Population Biology, Elsevier, vol. 76(2), pages 118-131.
    13. Maxim Finkelstein & Ji Hwan Cha, 2013. "Shocks as Burn-in," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 313-361, Springer.
    14. 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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    Cited by:

    1. Francisco Germán Badía & Sophie Mercier & Carmen Sangüesa, 2019. "Extensions of the Generalized Pólya Process," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1057-1085, December.

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