Two New Mathematical Equalities in the Life Table (original) (raw)
Canadian Studies in Population
This paper discusses known mathematical equalities and inequalities found within life tables and proceeds to identify two new inequalities. The first (theorem 1) is that at any given age x, the sum of mean years lived and mean years remaining exceeds life expectancy at birth when age is greater than zero and less than the maximum lifespan. The second inequality (theorem 2) applies to the entire population and shows that the sum of mean years lived and mean years remaining exceeds life expectancy at birth. Illustrations of the two inequalities are provided as well as a discussion. Résumé Cet article examine les égalités et les inégalités mathématiques connues dans les tables de mortalité et procède à l'identification de deux nouvelles inégalités. La premiére (théorème 1) est que,à tout âge x donné, la somme d'années moyennes vécues et d'années moyennes restantes dépasse l'espérance de vie à la naissance lorsque l'âge est supérieur à zéro et inférieur à la durée de vie maximale. La deuxième inégalité (théorème 2) s'applique à l'ensemble de la population et montre que la somme d'années moyennes vécues et d'années moyennes restantes dépasse l'espérance de vie à la naissance. Des illustrations des deux inégalités sont fournies ainsi qu'une discussion. Keywords Carey's Equality Theorem. Life years lost. Life expectancy at birth. Mean years lived. mean years remaining. variance in age at death Mots-clé théoréme d'égalité de Carey. années de vie perdues. espérance de vie à la naissance. nombre d'années vécues. nombre d'années restantes. variance de l'âge au décès
Sign up for access to the world's latest research.
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Related papers
On Mathematical Equalities and Inequalities in the Life Table: Something Old and Something New
Canadian Studies in Population
This paper discusses known mathematical equalities and inequalities found within life tables and proceeds to identify two new inequalities. The first (theorem 1) is that at any given age x, the sum of mean years lived and mean years remaining exceeds life expectancy at birth when age is greater than zero and less than the maximum lifespan. The second inequality (theorem 2) applies to the entire population and shows that the sum of mean years lived and mean years remaining exceeds life expectancy at birth. Illustrations of the two inequalities are provided as well as a discussion.
Expectation of life at old age predicted from a single death rate: Models and applications
2017
This paper introduces empirical relations between the death rate at a given age and the remaining life expectancy at that same age. The relations prove to be of prediction accuracy exceeding that of the common alternative, extrapolation of the death rates into older ages based on data at younger ages. Being close in accuracy to models by Horiuchi, Coale and Mitra, the proposed models may be of use in cases when the latter models may not be applied because of either lack of data on old-age mortality or violation of the underlying assumptions, such as population stability. Combining the proposed models with constrained extrapolations of old-age mortality will be a useful tool in estimating and projecting old-age mortality, completing life tables for young cohorts and extending model and empirical life tables to old age.
Inference on the endpoint of human lifespan and its inherent statistical difficulty
Extremes, 2018
We offer an inference methodology for the upper endpoint of a regularly varying distribution with finite endpoint. We apply it to the IDL and GRG data sets of lifespans of supercentenarians. As in the comprehensive analysis of Rootzén and Zholud, our results underscore the effect of the data sampling scheme and censoring on the conclusions. We also quantify the statistical difficulty of distinguishing between the hypotheses of finite and infinite lifespan by providing estimates of the required sample size. 1 The Bible, facts, and myths The question about whether the natural human lifespan has a hard biological limit has been of great interest since the beginning of time. Not surprisingly, therefore, the answer can be found in The Bible, Genesis (The Wickedness of Mankind), Ch 6:3 [1]: And the Lord said, My Spirit shall not always strive with man, for that he also is flesh: yet his days shall be a hundred and twenty years.
Proceedings of the National Academy of Sciences, 2003
The life expectancy implied by current age-specific mortality rates is calculated with life table methods that are among the oldest and most fundamental tools of demography. We demonstrate that these conventional estimates of period life expectancy are affected by an undesirable ''tempo effect.'' The tempo effect is positive when the mean age at death is rising and negative when the mean is declining. Estimates of the effect for females in three countries with high and rising life expectancy range from 1.6 yr in the U.S. and Sweden to 2.4 yr in France for the period 1980 -1995.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.