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Gompertz–Makeham life expectancies: Expressions and applications

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  • Missov, Trifon I.
  • Lenart, Adam

Abstract

In a population of individuals, whose mortality is governed by a Gompertz–Makeham hazard, we derive closed-form solutions to the life-expectancy integral, corresponding to the cases of homogeneous and gamma-heterogeneous populations, as well as in the presence/absence of the Makeham term. Derived expressions contain special functions that aid constructing high-accuracy approximations, which can be used to study the elasticity of life expectancy with respect to model parameters. Knowledge of Gompertz–Makeham life expectancies aids constructing life-table exposures.

Suggested Citation

  • Missov, Trifon I. & Lenart, Adam, 2013. "Gompertz–Makeham life expectancies: Expressions and applications," Theoretical Population Biology, Elsevier, vol. 90(C), pages 29-35.
    • Handle: RePEc:eee:thpobi:v:90:y:2013:i:c:p:29-35
    DOI: 10.1016/j.tpb.2013.09.013
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    References listed on IDEAS

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    1. Adam Lenart, 2012. "The Gompertz distribution and maximum likelihood estimation of its parameters - a revision," MPIDR Working Papers WP-2012-008, Max Planck Institute for Demographic Research, Rostock, Germany.
    2. 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.
    3. Michael Gurven & Hillard Kaplan, 2007. "Longevity Among Hunter‐ Gatherers: A Cross‐Cultural Examination," Population and Development Review, The Population Council, Inc., vol. 33(2), pages 321-365, June.
    4. 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.
    5. Shripad Tuljapurkar & Nan Li & Carl Boe, 2000. "A universal pattern of mortality decline in the G7 countries," Nature, Nature, vol. 405(6788), pages 789-792, June.
    6. Trifon Missov & Adam Lenart, 2011. "Linking period and cohort life-expectancy linear increases in Gompertz proportional hazards models," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 24(19), pages 455-468.
    7. 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.
    8. 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:

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    2. Dirk Lauinger & Romain G. Billy & Felipe Vásquez & Daniel B. Müller, 2021. "A general framework for stock dynamics of populations and built and natural environments," Journal of Industrial Ecology, Yale University, vol. 25(5), pages 1136-1146, October.
    3. Kulinskaya, Elena & Gitsels, Lisanne Andra & Bakbergenuly, Ilyas & Wright, Nigel R., 2021. "Dynamic hazards modelling for predictive longevity risk assessment," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 222-231.
    4. Kulinskaya, Elena & Gitsels, Lisanne A. & Bakbergenuly, Ilyas & Wright, Nigel R., 2020. "Calculation of changes in life expectancy based on proportional hazards model of an intervention," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 27-35.
    5. Jonas Šiaulys & Rokas Puišys, 2022. "Survival with Random Effect," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
    6. Ugofilippo Basellini & Vladimir Canudas-Romo & Adam Lenart, 2019. "Location–Scale Models in Demography: A Useful Re-parameterization of Mortality Models," European Journal of Population, Springer;European Association for Population Studies, vol. 35(4), pages 645-673, October.
    7. 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.

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