The Life Table Population Identity: Discovery, Formulations, Proof, Extensions, and Applications

James R. Carey, Sarah Silverman, Arni S.R. Srinivasa Rao

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Scopus citations


The life table population identity was first discovered by Nicolas Brouard in the mid-1980s but brought into the mainstream demographic literature when rediscovered by James Carey in the early 2000s in the context of fruit fly demography. Based on the assumption of stationarity, the identity states that the fraction age x in a population equals the fraction with x years to live. The purpose of this chapter is to describe the contexts within which both Brouard and Carey discovered the identity, present a proof, three extensions, and two applications, the latter of which involves estimation of mean age and age structure in wild fruit fly populations. At the end we discuss the relevance of the identity to demography in general and to human demography in particular.

Original languageEnglish (US)
Title of host publicationHandbook of Statistics
EditorsArni S.R. Srinivasa Rao, C.R. Rao
PublisherElsevier B.V.
Number of pages32
ISBN (Print)9780444640727
Publication statusPublished - Jan 1 2018

Publication series

NameHandbook of Statistics
ISSN (Print)0169-7161



  • Age-structure theorems
  • Brouard's Theorem
  • Carey's Equality
  • Life table populations
  • Nonstationary populations
  • Stationary populations

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

Cite this

Carey, J. R., Silverman, S., & Srinivasa Rao, A. S. R. (2018). The Life Table Population Identity: Discovery, Formulations, Proof, Extensions, and Applications. In A. S. R. Srinivasa Rao, & C. R. Rao (Eds.), Handbook of Statistics (pp. 155-186). (Handbook of Statistics; Vol. 39). Elsevier B.V..