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The Gompertz distribution and maximum likelihood estimation of its parameters - a revision

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  • Adam Lenart

    (Max Planck Institute for Demographic Research, Rostock, Germany)

Abstract

The Gompertz distribution is widely used to describe the distribution of adult deaths. Previous works concentrated on formulating approximate relationships to characterize it. However, using the generalized integro-exponential function Milgram (1985) exact formulas can be derived for its moment-generating function and central moments. Based on the exact central moments, higher accuracy approximations can be defined for them. In demographic or actuarial applications, maximum-likelihood estimation is often used to determine the parameters of the Gompertz distribution. By solving the maximum-likelihood estimates analytically, the dimension of the optimization problem can be reduced to one both in the case of discrete and continuous data.

Suggested Citation

  • 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.
    • Handle: RePEc:dem:wpaper:wp-2012-008
    DOI: 10.4054/MPIDR-WP-2012-008
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    Cited by:

    1. S. Nadarajah & S. Bakar, 2013. "A new R package for actuarial survival models," Computational Statistics, Springer, vol. 28(5), pages 2139-2160, October.
    2. Zangin Zeebari & Kristofer Månsson & Pär Sjölander & Magnus Söderberg, 2023. "Regularized conditional estimators of unit inefficiency in stochastic frontier analysis, with application to electricity distribution market," Journal of Productivity Analysis, Springer, vol. 59(1), pages 79-97, February.
    3. Missov, Trifon I. & Lenart, Adam, 2013. "Gompertz–Makeham life expectancies: Expressions and applications," Theoretical Population Biology, Elsevier, vol. 90(C), pages 29-35.

    More about this item

    JEL classification:

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

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