Volume 24 - Article 11 | Pages 251–256  

Life expectancy: Lower and upper bounds from surviving fractions and remaining life expectancy

By Joel E. Cohen

This article is part of the ongoing Special Collection 8 „Formal Relationships“

Abstract

We give simple upper and lower bounds on life expectancy. In a life-table population, if e(0) is the life expectancy at birth, M is the median length of life, and e(M) is the expected remaining life at age M, then (M+e(M))/2≤e(0)≤M+e(M)/2. In general, for any age x, if e(x) is the expected remaining life at age x, and ℓ(x) is the fraction of a cohort surviving to age x at least, then (x+e(x))≤l(x)≤e(0)≤x+l(x)∙e(x). For any two ages 0≤w≤x≤ω, (x-w+e(x))∙ℓ(x)/ℓ(w)≤e(w)≤x-w+e(x)∙ℓ(x)/ℓ(w) . These inequalities give bounds on e(0) without detailed knowledge of the course of mortality prior to age x, provided ℓ(x) can be estimated. Such bounds could be useful for estimating life expectancy where the input of eggs or neonates can be estimated but mortality cannot be observed before late juvenile or early adult ages.

Author’s Affiliation

• Joel E. Cohen - Rockefeller University, United States of America EMAIL

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 is the death-weighted average of the reciprocal of the survival-specific force of mortality
Volume 22 - Article 5

Constant global population with demographic heterogeneity
Volume 18 - Article 14

Most recent similar articles in Demographic Research

Modifying model life tables to derive mortality curves for countries with excess mortality
Volume 53 - Article 2    | Keywords: armed conflict, Colombia, homicide, life expectancy, probability of dying, road traffic accidents, violence, war

Life expectancy by religious affiliation in Finland 1972–2020
Volume 52 - Article 17    | Keywords: Finland, life expectancy, register data, religious affiliation

The impact of the COVID-19 pandemic on mortality in Uruguay from 2020 to 2022
Volume 51 - Article 29    | Keywords: COVID-19, excess mortality, life expectancy, Uruguay

Higher incomes are increasingly associated with higher fertility: Evidence from the Netherlands, 2008–2022
Volume 51 - Article 26    | Keywords: fertility, income, inequalities, Netherlands, parenthood

On the relationship between life expectancy, modal age at death, and the threshold age of the life table entropy
Volume 51 - Article 24    | Keywords: Gompertz law, life expectancy, lifespan variation, longevity, mode, mortality