TY - JOUR
T1 - Symmetries between life lived and left in finite stationary populations
AU - Villavicencio, Francisco
AU - Riffe, Tim
N1 - Funding Information:
We are both grateful to Jim Vaupel for arousing and encouraging our interest in formal demography, and for his support in this project. We would also like to thank Fernando Colchero, Josh Goldstein, and two anonymous reviewers for critical and helpful comments. Part of this work was carried out while TR was at the Department of Demography, University of California, Berkeley. This research was partially supported by a grant from the SDU eScience Center and by grants No. R01-AG011552 and R01-AG040245 of the U.S. National Institute on Aging of the National Institutes of Health. The content is solely the responsibility of the authors and does not necessarily represent the official views of the funding agencies.
Publisher Copyright:
© 2016 Francisco Villavicencio & Tim Riffe.
PY - 2016
Y1 - 2016
N2 - Background The Brouard-Carey equality describes the symmetries between the distribution of life lived and life left in stationary populations. This result was formally proved for populations of infinite size and continuous time, and a subsequent attempt to prove it for populations of finite size is invalid. Objective We attempt to provide a formal mathematical proof of the Brouard-Carey equality for finite stationary populations. Conclusions The symmetries between life lived and life left in finite stationary populations can only be proved if time is explicitly discretized. The proof is more complex than in a continuoustime framework, but it conforms with the kinds of data usually available to researchers. CONTRIBUTION The main contribution of this paper is to offer a complete and formal proof of the symmetries between life lived and life left for finite stationary populations in a discrete-time framework. This result is a useful tool for the study of human and non-human populations when the assumption of stationarity is acceptable, especially when subject ages are unknown, but individuals are followed-up until death.
AB - Background The Brouard-Carey equality describes the symmetries between the distribution of life lived and life left in stationary populations. This result was formally proved for populations of infinite size and continuous time, and a subsequent attempt to prove it for populations of finite size is invalid. Objective We attempt to provide a formal mathematical proof of the Brouard-Carey equality for finite stationary populations. Conclusions The symmetries between life lived and life left in finite stationary populations can only be proved if time is explicitly discretized. The proof is more complex than in a continuoustime framework, but it conforms with the kinds of data usually available to researchers. CONTRIBUTION The main contribution of this paper is to offer a complete and formal proof of the symmetries between life lived and life left for finite stationary populations in a discrete-time framework. This result is a useful tool for the study of human and non-human populations when the assumption of stationarity is acceptable, especially when subject ages are unknown, but individuals are followed-up until death.
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U2 - 10.4054/DemRes.2016.35.14
DO - 10.4054/DemRes.2016.35.14
M3 - Article
AN - SCOPUS:85006942907
SN - 1435-9871
VL - 35
SP - 381
EP - 398
JO - Demographic Research
JF - Demographic Research
ER -