On some stochastic properties of lives lived and left in non-stationary populations

Maxim Finkelstein*, James Vaupel

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

First, we revisit the “life lived equals life left” property for stationary populations and discuss it from a more general perspective. Specifically, we show that identically distributed random age and the remaining lifetime in stationary populations have the same distribution as the equilibrium distribution of the renewal theory. Then we consider specific non-stationary populations that are closed to migration and have a constant birth rate. We obtain some useful inequalities between random age and remaining lifetime for different instants of calendar time. We also discuss the aging properties of populations using different stochastic orders.

Original languageEnglish
JournalJournal of Mathematical Biology
Volume80
Issue number6
Pages (from-to)1845-1856
ISSN0303-6812
DOIs
Publication statusPublished - May 2020

Keywords

  • Equilibrium distribution
  • Random age
  • Remaining lifetime
  • Stationary population
  • Stochastic ordering

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