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On closed-form expressions to Gompertz–Makeham life expectancy

Author

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  • Castellares, Fredy
  • Patrício, Silvio C.
  • Lemonte, Artur J.
  • Queiroz, Bernardo L.

Abstract

Missov and Lenart (2013) derived closed-form solutions to the life expectancy and remaining life expectancy at age x when the mortality is governed by a Gompertz–Makeham hazard, which is a parametric model commonly applied to human mortality data at adult and old ages. However, the closed-form expressions provided by these authors are not correct. We provide, therefore, valid and correct expressions using elementary calculus. We also consider numerical studies using real data to show that the formulas we provide deliver satisfactory results.

Suggested Citation

  • Castellares, Fredy & Patrício, Silvio C. & Lemonte, Artur J. & Queiroz, Bernardo L., 2020. "On closed-form expressions to Gompertz–Makeham life expectancy," Theoretical Population Biology, Elsevier, vol. 134(C), pages 53-60.
    • Handle: RePEc:eee:thpobi:v:134:y:2020:i:c:p:53-60
    DOI: 10.1016/j.tpb.2020.04.005
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    References listed on IDEAS

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    1. Missov, Trifon I. & Lenart, Adam, 2013. "Gompertz–Makeham life expectancies: Expressions and applications," Theoretical Population Biology, Elsevier, vol. 90(C), pages 29-35.
    2. Trifon Missov, 2013. "Gamma-Gompertz life expectancy at birth," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 28(9), pages 259-270.
    3. Scrucca, Luca, 2013. "GA: A Package for Genetic Algorithms in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 53(i04).
    4. Böhnstedt, Marie & Gampe, Jutta, 2019. "Detecting mortality deceleration: Likelihood inference and model selection in the gamma-Gompertz model," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 68-73.
    5. 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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