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Admissible mixing distributions for a general class of mixture survival models with known asymptotics

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  • Missov, Trifon I.
  • Finkelstein, Maxim

Abstract

Statistical analysis of data on the longest living humans leaves room for speculation whether the human force of mortality is actually leveling off. Based on this uncertainty, we study a mixture failure model, introduced by Finkelstein and Esaulova (2006) that generalizes, among others, the proportional hazards and accelerated failure time models. In this paper we first, extend the Abelian theorem of these authors to mixing distributions, whose densities are functions of regular variation. In addition, taking into account the asymptotic behavior of the mixture hazard rate prescribed by this Abelian theorem, we prove three Tauberian-type theorems that describe the class of admissible mixing distributions. We illustrate our findings with examples of popular mixing distributions that are used to model unobserved heterogeneity.

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  • 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.
    • Handle: RePEc:eee:thpobi:v:80:y:2011:i:1:p:64-70
    DOI: 10.1016/j.tpb.2011.05.001
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    Cited by:

    1. 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.
    2. 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.
    3. Adriaan Kalwij, 2014. "An empirical analysis of the importance of controlling for unobserved heterogeneity when estimating the income-mortality gradient," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 31(30), pages 913-940.
    4. Missov, Trifon I. & Lenart, Adam, 2013. "Gompertz–Makeham life expectancies: Expressions and applications," Theoretical Population Biology, Elsevier, vol. 90(C), pages 29-35.
    5. Finkelstein, Maxim, 2012. "On ordered subpopulations and population mortality at advanced ages," Theoretical Population Biology, Elsevier, vol. 81(4), pages 292-299.
    6. Hal Caswell, 2014. "A matrix approach to the statistics of longevity in heterogeneous frailty models," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 31(19), pages 553-592.
    7. Elizabeth Wrigley-Field, 2013. "Mortality deceleration is not informative of unobserved heterogeneity in open groups," Vienna Yearbook of Population Research, Vienna Institute of Demography (VID) of the Austrian Academy of Sciences in Vienna, vol. 11(1), pages 15-36.
    8. Maxim S. Finkelstein, 2011. "On ordered subpopulations and population mortality at advanced ages," MPIDR Working Papers WP-2011-022, Max Planck Institute for Demographic Research, Rostock, Germany.
    9. 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.
    10. Yann Le Cunff & Annette Baudisch & Khashayar Pakdaman, 2013. "How Evolving Heterogeneity Distributions of Resource Allocation Strategies Shape Mortality Patterns," PLOS Computational Biology, Public Library of Science, vol. 9(1), pages 1-14, January.
    11. Elizabeth Wrigley-Field, 2014. "Mortality Deceleration and Mortality Selection: Three Unexpected Implications of a Simple Model," Demography, Springer;Population Association of America (PAA), vol. 51(1), pages 51-71, February.
    12. Cha, Ji Hwan & Finkelstein, Maxim, 2014. "Some notes on unobserved parameters (frailties) in reliability modeling," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 99-103.
    13. Virginia Zarulli, 2016. "Unobserved Heterogeneity of Frailty in the Analysis of Socioeconomic Differences in Health and Mortality," European Journal of Population, Springer;European Association for Population Studies, vol. 32(1), pages 55-72, February.
    14. 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.
    15. Giambattista Salinari & Gustavo De Santis, 2020. "One or more rates of ageing? The extended gamma-Gompertz model (EGG)," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 211-236, June.

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