Two New Mathematical Equalities in the Life Table

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.