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

 Date received: 12 Nov 2013 Date published: 07 May 2014 Word count: 770 Keywords: life disparity, life table entropy, remaining life expectancy, variance in age at death DOI: 10.4054/DemRes.2014.30.50 Weblink: All publications in the ongoing Special Collection 8 "Formal Relationships" can be found at http://www.demographic-research.org/special/8/

## 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.

## Author's Affiliation

- Max-Planck-Institut für Demografische Forschung, Germany [Email]

## Other articles by the same author/authors in Demographic Research

» The pace of aging: Intrinsic time scales in demography
Volume 30 - Article 57

» Entropy of the Gompertz-Makeham mortality model
Volume 30 - Article 49

» How life expectancy varies with perturbations in age-specific mortality
Volume 27 - Article 13

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