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

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  • W.J. Willemse
  • R. Kaas
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    Abstract

    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.

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    File URL: http://www.dnb.nl/binaries/Working%20Paper%20135-2007_tcm46-146792.pdf
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    Bibliographic Info

    Paper provided by Netherlands Central Bank, Research Department in its series DNB Working Papers with number 135.

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    Date of creation: Apr 2007
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    Handle: RePEc:dnb:dnbwpp:135

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    Related research

    Keywords: Heterogeneous mortality models; Frailty models; Gompertz distribution; Identifiability.;

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    1. S. Olshansky & Bruce Carnes, 1997. "Ever since gompertz," Demography, Springer, 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, vol. 16(3), pages 439-454, August.
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