@inbook{e798f788217542d6a04dd239613d2c25,

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

abstract = "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.",

keywords = "Age-structure theorems, Brouard's Theorem, Carey's Equality, Life table populations, Nonstationary populations, Stationary populations",

author = "Carey, {James R.} and Sarah Silverman and {Srinivasa Rao}, {Arni S.R.}",

note = "Funding Information: Many of the findings that inform this chapter were supported in part by grants from the National Institute on Aging (NIA/NIH) P01 AG0225001-01 and AG08761-10, and through the UC Berkeley CEDA grant P30AG0128. We thank Tim Riffe for bringing Brouard's Theorem to our attention and, along with Francisco Villavicencio and Michel Guillot, for their insightful and constructive comments on an earlier version of this paper. We are grateful to Nicolas Brouard for background information he provided us about the circumstances of his original discovery and to Lawrence Harshman for his ideas concerning the practical implications of the life table identity. Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

year = "2018",

month = jan,

day = "1",

doi = "10.1016/bs.host.2018.08.002",

language = "English (US)",

isbn = "9780444640727",

series = "Handbook of Statistics",

publisher = "Elsevier B.V.",

pages = "155--186",

editor = "{Srinivasa Rao}, {Arni S.R.} and C.R. Rao",

booktitle = "Handbook of Statistics",

}