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Variance in age at death equals average squared remaining life expectancy at death

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  • Tomasz Wrycza

    (Max-Planck-Institut für Demografische Forschung)

Abstract

Background: Variance in lifespan $\sigma^2$ and life expectancy lost due to death $e^{\dagger}$ are important demographic indicators of life disparity. Objective: I show that variance in age at death equals average squared remaining life expectancy at death. Based on this I also show that the average squared difference in remaining life expectancy at death equals the difference between $\sigma^2$ and ${e^{\dagger}}^2$. Comments: Calculations of the quantities involved for the Gompertz-Makeham mortality model with varying parameters reveals complex patterns.

Suggested Citation

  • Tomasz Wrycza, 2014. "Variance in age at death equals average squared remaining life expectancy at death," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(50), pages 1405-1412.
    • Handle: RePEc:dem:demres:v:30:y:2014:i:50
    DOI: 10.4054/DemRes.2014.30.50
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    References listed on IDEAS

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    1. Nathan Keyfitz, 1977. "What difference would it make if cancer were eradicated? An examination of the taeuber paradox," Demography, Springer;Population Association of America (PAA), vol. 14(4), pages 411-418, November.
    2. S. Mitra, 1978. "A short note on the taeuber paradox," Demography, Springer;Population Association of America (PAA), vol. 15(4), pages 621-623, November.
    3. Joshua R. Goldstein, 2009. "Life lived equals life left in stationary populations," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 20(2), pages 3-6.
    4. Noreen Goldman & Graham Lord, 1986. "A new look at entropy and the life table," Demography, Springer;Population Association of America (PAA), vol. 23(2), pages 275-282, May.
    5. James W. Vaupel, 2010. "Total daily change with age equals average lifetime change," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 22(36), pages 1143-1148.
    6. Alyson Raalte & Hal Caswell, 2013. "Perturbation Analysis of Indices of Lifespan Variability," Demography, Springer;Population Association of America (PAA), vol. 50(5), pages 1615-1640, October.
    7. 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.
    8. Ryan D. Edwards & Shripad Tuljapurkar, 2005. "Inequality in Life Spans and a New Perspective on Mortality Convergence Across Industrialized Countries," Population and Development Review, The Population Council, Inc., vol. 31(4), pages 645-674, December.
    9. Shripad Tuljapurkar & Ryan Edwards, 2011. "Variance in death and its implications for modeling and forecasting mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 24(21), pages 497-526.
    10. Zhen Zhang & James W. Vaupel, 2009. "The age separating early deaths from late deaths," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 20(29), pages 721-730.
    11. Zhen Zhang & James W. Vaupel, 2009. "The age separating early deaths from late deaths," MPIDR Working Papers WP-2009-004, Max Planck Institute for Demographic Research, Rostock, Germany.
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    1. Jacob Martin & Iñaki Permanyer & Jose Manuel Aburto, 2023. "Dynamics of the coefficient of variation of the age at death distribution," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 49(38), pages 1063-1086.

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    More about this item

    Keywords

    life disparity; remaining life expectancy; life table entropy; variance in age at death;
    All these keywords.

    JEL classification:

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

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