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Gamma-Gompertz life expectancy at birth

Author

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  • Trifon Missov

    (Syddansk Universitet)

Abstract

Background: The gamma-Gompertz multiplicative frailty model is the most common parametric model applied to human mortality data at adult and old ages. The resulting life expectancy has been calculated so far only numerically. Objective: Properties of the gamma-Gompertz distribution have not been thoroughly studied. The focus of the paper is to shed light onto its first moment or, demographically speaking, characterize life expectancy resulting from a gamma-Gompertz force of mortality. The paper provides an exact formula for gamma-Gompertz life expectancy at birth and a simpler high-accuracy approximation that can be used in practice for computational convenience. In addition, the article compares actual (life-table) to model-based (gamma-Gompertz) life expectancy to assess on aggregate how many years of life expectancy are not captured (or overestimated) by the gamma-Gompertz mortality mechanism. Comments: A closed-form expression for gamma-Gomeprtz life expectancy at birth contains a special (the hypergeometric) function. It aids assessing the impact of gamma-Gompertz parameters on life expectancy values. The paper shows that a high-accuracy approximation can be constructed by assuming an integer value for the shape parameter of the gamma distribution. A historical comparison between model-based and actual life expectancy for Swedish females reveals a gap that is decreasing to around 2 years from 1950 onwards. Looking at remaining life expectancies at ages 30 and 50, we see this gap almost disappearing.

Suggested Citation

  • 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.
    • Handle: RePEc:dem:demres:v:28:y:2013:i:9
    DOI: 10.4054/DemRes.2013.28.9
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    References listed on IDEAS

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    1. 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. Lucia Zanotto & Vladimir Canudas-Romo & Stefano Mazzuco, 2021. "A Mixture-Function Mortality Model: Illustration of the Evolution of Premature Mortality," European Journal of Population, Springer;European Association for Population Studies, vol. 37(1), pages 1-27, March.
    2. 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.
    3. Castellares, Fredy & Patrício, Silvio C. & Lemonte, Artur J., 2020. "On gamma-Gompertz life expectancy," Statistics & Probability Letters, Elsevier, vol. 165(C).
    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. 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.
    6. Jonas Šiaulys & Rokas Puišys, 2022. "Survival with Random Effect," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
    7. María-Dolores Huete-Morales & Esteban Navarrete-Álvarez & María-Jesús Rosales-Moreno & María-José Del-Moral-Ávila & José-Manuel Quesada-Rubio, 2020. "Modelling the survival function of the Spanish population by the Wong–Tsui model with the incorporation of frailty and covariates," Letters in Spatial and Resource Sciences, Springer, vol. 13(2), pages 151-163, August.
    8. 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.
    9. 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.
    10. Bijwaard, G.E.; & Jones, A.M.;, 2019. "Education and life-expectancy and how the relationship is mediated through changes in behaviour: a principal stratification approach for hazard rates," Health, Econometrics and Data Group (HEDG) Working Papers 19/05, HEDG, c/o Department of Economics, University of York.

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    More about this item

    Keywords

    life expectancy at birth; gamma-Gompertz frailty model; hypergeometric function; life expectancy;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

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