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Rational reconstruction of frailty-based mortality models by a generalisation of Gompertz' law of mortality


  • W.J. Willemse
  • R. Kaas


A generalisation of Gompertz' distribution is proposed, and it is shown that continuous heterogeneous mortality models with Gamma distributed frailty have lifetime random variables distributed as the difference of two such generalised Gompertz random variables. With this result, limitations of existing frailty-based mortality models are identified. The approach taken in this paper allows the frailty distribution to be interpreted as a lifetime reduction distribution and enables application of heterogeneous survival models with a stronger relation to empirically identifiable concepts.

Suggested Citation

  • W.J. Willemse & R. Kaas, 2007. "Rational reconstruction of frailty-based mortality models by a generalisation of Gompertz' law of mortality," DNB Working Papers 135, Netherlands Central Bank, Research Department.
  • Handle: RePEc:dnb:dnbwpp:135

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    References listed on IDEAS

    1. S. Olshansky & Bruce Carnes, 1997. "Ever since gompertz," Demography, Springer;Population Association of America (PAA), vol. 34(1), pages 1-15, February.
    2. 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. Milevsky, Moshe A., 2020. "Calibrating Gompertz in reverse: What is your longevity-risk-adjusted global age?," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 147-161.
    2. Alexander, Monica, 2018. "Deaths without denominators: using a matched dataset to study mortality patterns in the United States," SocArXiv q79ye, Center for Open Science.

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    More about this item


    Heterogeneous mortality models; Frailty models; Gompertz distribution; Identifiability.;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts

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