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Understanding Mortality Rate Deceleration and Heterogeneity

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  • David Steinsaltz
  • Kenneth Wachter

Abstract

Generic relationships between heterogeneity in population frailty and flattening of aggregate population hazard functions at extreme ages are drawn from classical mathematical results on the limiting behavior of Laplace transforms. In particular, it shows that the population hazard function converges to a constant precisely when the distribution of unobserved heterogeneity in initial mortalities behaves asymptotically as a polynomial near zero.

Suggested Citation

  • David Steinsaltz & Kenneth Wachter, 2006. "Understanding Mortality Rate Deceleration and Heterogeneity," Mathematical Population Studies, Taylor & Francis Journals, vol. 13(1), pages 19-37.
    • Handle: RePEc:taf:mpopst:v:13:y:2006:i:1:p:19-37
    DOI: 10.1080/08898480500452117
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    Citations

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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. Adrian Raftery & Jennifer Chunn & Patrick Gerland & Hana Ševčíková, 2013. "Bayesian Probabilistic Projections of Life Expectancy for All Countries," Demography, Springer;Population Association of America (PAA), vol. 50(3), pages 777-801, June.
    4. Elizabeth Wrigley-Field, 2020. "Multidimensional Mortality Selection: Why Individual Dimensions of Frailty Don’t Act Like Frailty," Demography, Springer;Population Association of America (PAA), vol. 57(2), pages 747-777, April.
    5. 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.
    6. Maxim Finkelstein, 2009. "‘Understanding the shape of the mixture failure rate’ Rejoinder by Maxim Finkelstein," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(6), pages 673-677, November.
    7. Annamaria Olivieri & Ermanno Pitacco, 2016. "Frailty and Risk Classification for Life Annuity Portfolios," Risks, MDPI, vol. 4(4), pages 1-23, October.
    8. Kenneth Manton & Igor Akushevich & Alexander Kulminski, 2008. "Human Mortality at Extreme Ages: Data from the NLTCS and Linked Medicare Records," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(3), pages 137-159.
    9. Alberto Palloni & Hiram Beltrán-Sánchez, 2017. "Discrete Barker Frailty and Warped Mortality Dynamics at Older Ages," Demography, Springer;Population Association of America (PAA), vol. 54(2), pages 655-671, April.
    10. Finkelstein, Maxim, 2012. "On ordered subpopulations and population mortality at advanced ages," Theoretical Population Biology, Elsevier, vol. 81(4), pages 292-299.
    11. Kenneth W. Wachter, 2008. "Biodemography comes of Age," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 19(40), pages 1501-1512.
    12. László Németh & Trifon I Missov, 2018. "Adequate life-expectancy reconstruction for adult human mortality data," PLOS ONE, Public Library of Science, vol. 13(6), pages 1-8, June.
    13. Maxim S. Finkelstein, 2009. "Understanding the shape of the mixture failure rate (with engineering and demographic applications)," MPIDR Working Papers WP-2009-031, Max Planck Institute for Demographic Research, Rostock, Germany.
    14. Hartemink, Nienke & Missov, Trifon I. & Caswell, Hal, 2017. "Stochasticity, heterogeneity, and variance in longevity in human populations," Theoretical Population Biology, Elsevier, vol. 114(C), pages 107-116.
    15. Maxim Finkelstein, 2009. "Understanding the shape of the mixture failure rate (with engineering and demographic applications)," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(6), pages 643-663, November.
    16. 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.
    17. 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.
    18. MARK BEBBINGTON & CHIN-DIEW LAI & RIcARDAS ZITIKIS, 2011. "Modelling Deceleration in Senescent Mortality," Mathematical Population Studies, Taylor & Francis Journals, vol. 18(1), pages 18-37.
    19. 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.
    20. Dennis M. Feehan, 2018. "Separating the Signal From the Noise: Evidence for Deceleration in Old-Age Death Rates," Demography, Springer;Population Association of America (PAA), vol. 55(6), pages 2025-2044, December.

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