In a Stationary Population, the Average Lifespan of the Living Is a Length-Biased Life Expectancy

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1 Scopus citations


What is the average lifespan in a stationary population viewed at a single moment in time? Even though periods and cohorts are identical in a stationary population, we show that the answer to this question is not life expectancy but a length-biased version of life expectancy. That is, the distribution of lifespans of the people alive at a single moment is a self-weighted distribution of cohort lifespans, such that longer lifespans have proportionally greater representation. One implication is that if death rates are unchanging, the average lifespan of the current population always exceeds period life expectancy. This result connects stationary population lifespan measures to a well-developed body of statistical results; provides new intuition for established demographic results; generates new insights into the relationship between periods, cohorts, and prevalent cohorts; and offers a framework for thinking about mortality selection more broadly than the concept of demographic frailty.

Original languageEnglish (US)
Pages (from-to)207-220
Number of pages14
Issue number1
StatePublished - Feb 1 2022

Bibliographical note

Funding Information:
Acknowledgments The authors gratefully acknowledge support from the Eunice Kennedy Shriver Institute for Child Health and Human Development via the Minnesota Population Center (P2C HD041023) and Berkeley Population Center (P2C HD073964); from the National Institute of Aging via the Life Course Center for the Demography and Economics of Aging (P30 AG066613); and from the Fesler-Lampert Chair in Aging Studies at the University of Minnesota; as well as helpful comments from Felix Elwert, Michelle Niemann, James Vaupel, and several anonymous reviewers.

Publisher Copyright:
© 2021 The Authors.


  • Length-biased sampling
  • Life expectancy
  • Mortality selection
  • Prevalent cohort
  • Size bias

PubMed: MeSH publication types

  • Journal Article
  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't


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