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On a closed-form expression and its approximation to Gompertz life disparity

Author

Listed:
  • Cinzia Di Palo

    (Università degli Studi di Cassino e del Lazio Meridionale)

Abstract

Background: In the literature, there exists a closed form solution to the remaining life expectancy at age x when mortality is governed by the Gompertz law. This expression contains a special function that allows us to construct high-accuracy approximations, which are also helpful in assessing the elasticity of life expectancy with respect to the model parameters. However, to my knowledge, a similar formulation for life disparity does not exist, and as a consequence, it does not exist for life table entropy either. Contribution: Under the assumption that mortality is governed by the Gompertz law, I present and prove a closed form expression for life disparity at age x that is similar to that existing for life expectancy. Since the closed form expressions hold for both life expectancy and life disparity, an exact expression for the life table entropy is immediately derived. In addition, using known relationships on the exponential integral function, an approximate form for life disparity is also obtained.

Suggested Citation

  • Cinzia Di Palo, 2023. "On a closed-form expression and its approximation to Gompertz life disparity," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 49(1), pages 1-12.
    • Handle: RePEc:dem:demres:v:49:y:2023:i:1
    DOI: 10.4054/DemRes.2023.49.1
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    References listed on IDEAS

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    1. Maxim Finkelstein & James W. Vaupel, 2009. "Survival as a Function of Life Expectancy," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 21(29), pages 879-884.
    2. Shiro Horiuchi & John Wilmoth, 1998. "Deceleration in the age pattern of mortality at olderages," Demography, Springer;Population Association of America (PAA), vol. 35(4), pages 391-412, November.
    3. James Vaupel & Vladimir Romo, 2003. "Decomposing change in life expectancy: A bouquet of formulas in honor of Nathan Keyfitz’s 90th birthday," Demography, Springer;Population Association of America (PAA), vol. 40(2), pages 201-216, May.
    4. Jose Manuel Aburto & Jesús-Adrián Alvarez & Francisco Villavicencio & James W. Vaupel, 2019. "The threshold age of the lifetable entropy," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 41(4), pages 83-102.
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    More about this item

    Keywords

    life disparity; life table; entropy; exponential integral functions;
    All these keywords.

    JEL classification:

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

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