Volume 22 - Article 5 | Pages 115–128
Life expectancy is the death-weighted average of the reciprocal of the survival-specific force of mortality
Date received: | 08 Jun 2009 |
Date published: | 22 Jan 2010 |
Word count: | 2097 |
Keywords: | age-structured population, force of mortality, Jensen´s inequality, life expectancy, life table, longevity, negative exponential distribution, survival, United States of America |
DOI: | 10.4054/DemRes.2010.22.5 |
Weblink: | All publications in the ongoing Special Collection 8 "Formal Relationships" can be found at http://www.demographic-research.org/special/8/ |
Abstract
The hazard of mortality is usually presented as a function of age, but can be defined as a function of the fraction of survivors. This definition enables us to derive new relationships for life expectancy. Specifically, in a life-table population with a positive age-specific force of mortality at all ages, the expectation of life at age x is the average of the reciprocal of the survival-specific force of mortality at ages after x, weighted by life-table deaths at each age after x, as shown in (6). Equivalently, the expectation of life when the surviving fraction in the life table is s is the average of the reciprocal of the survival-specific force of mortality over surviving proportions less than s, weighted by life-table deaths at surviving proportions less than s, as shown in (8). Application of these concepts to the 2004 life tables of the United States population and eight subpopulations shows that usually the younger the age at which survival falls to half (the median life length), the longer the life expectancy at that age, contrary to what would be expected from a negative exponential life table.
Author's Affiliation
Joel E. Cohen - Rockefeller University, United States of America
Other articles by the same author/authors in Demographic Research
»
Measuring the concentration of urban population in the negative exponential model using the Lorenz curve, Gini coefficient, Hoover dissimilarity index, and relative entropy
Volume 44 - Article 49
»
Gompertz, Makeham, and Siler models explain Taylor's law in human mortality data
Volume 38 - Article 29
»
Taylor's power law in human mortality
Volume 33 - Article 21
»
Is the fraction of people ever born who are currently alive rising or falling?
Volume 30 - Article 56
»
Life expectancy: Lower and upper bounds from surviving fractions and remaining life expectancy
Volume 24 - Article 11
»
Constant global population with demographic heterogeneity
Volume 18 - Article 14
Most recent similar articles in Demographic Research
»
Survival as a Function of Life Expectancy
Volume 21 - Article 29 | Keywords: force of mortality, life expectancy, life table
»
Distributionally adjusted life expectancy as a life table function
Volume 43 - Article 14 | Keywords: life expectancy, life table
»
The impact of the choice of life table statistics when forecasting mortality
Volume 41 - Article 43 | Keywords: life expectancy, life table
»
The impact of proportional changes in age-specific mortality on life expectancy when the mortality rate is a log-linear function of age
Volume 39 - Article 23 | Keywords: force of mortality, life expectancy
»
The magnitude and timing of grandparental coresidence during childhood in the United States
Volume 37 - Article 52 | Keywords: life table, United States of America
Articles
Citations
Cited References: 2
»View the references of this article
Download to Citation Manager
Similar Articles
PubMed
Google Scholar