On Mathematical Equalities and Inequalities in the Life Table: Something Old and Something New (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.
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Two New Mathematical Equalities in the Life Table
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
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