Abstract
There is a rich body of literature on equalities in the period life table, which also can be interpreted as a stationary population, and a smaller, but no less rich, body on inequalities. The latter is important because it provides information on health disparities and, like the equality literature, serves as a foundation for formal mortality analysis. We straddle both of these bodies by reconciling a known inequality such that a new mathematical equality emerges in the period life table. We then show that this new equality links life expectancy at birth (mean age at death) directly to the average lifespan of the living members of a stationary population. This linkage represents a second newly identified equality in this paper that has the potential to yield useful insights because it links the average lifespan of the living members of a stationary population directly to elements that are central to the dynamics and structure of a stationary population, life expectancy, and variance in age at death.
Il existe de nombreuses études ayant trait aux équations dans les tables de mortalité du moment, c’est-à-dire s’appliquant à une population stationnaire. D’autres, moins nombreuses mais tout aussi pertinentes, s’intéressent quant à elles aux inéquations afférentes. Ces dernières sont essentielles puisqu’elles permettent de fournir de l’information sur les écarts en matière de santé et, conjointement aux premières, de fonder une analyse formelle de la mortalité. Nous concilions ces deux domaines de recherche en résolvant une inéquation déjà connue afin de dégager une nouvelle équation mathématique jamais encore identifiée dans les tables de mortalité du moment. Nous montrons ensuite que cette nouvelle équation établit un lien direct entre l’espérance de vie à la naissance (l’âge moyen au décès) et la durée de vie moyenne des membres vivants d’une population stationnaire. Cette relation constitue la deuxième nouvelle équation identifiée dans cet article qui, en établissant un rapport direct entre la durée de vie moyenne des membres vivants d’une population stationnaire et les éléments essentiels à sa dynamique et à sa structure, l’espérance de vie et la variance de l’âge au décès, pourrait permettre de fournir plusieurs renseignements utiles.
Change history
01 June 2022
A Correction to this paper has been published: https://doi.org/10.1007/s42650-022-00067-1
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We are grateful for comments from Jack Baker, Jeff Tayman, Richard Verdugo, three anonymous reviewers, and the editor.
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Swanson, D.A., Tedrow, L.M. Two New Mathematical Equalities in the Life Table. Can. Stud. Popul. 49, 67–73 (2022). https://doi.org/10.1007/s42650-022-00065-3
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DOI: https://doi.org/10.1007/s42650-022-00065-3