Variance in age at death equals average squared remaining life expectancy at death

Abstract

Background: Variance in lifespan $\sigma^2$ and life expectancy lost due to death $e^{\dagger}$ are important demographic indicators of life disparity. Objective: I show that variance in age at death equals average squared remaining life expectancy at death. Based on this I also show that the average squared difference in remaining life expectancy at death equals the difference between $\sigma^2$ and ${e^{\dagger}}^2$. Comments: Calculations of the quantities involved for the Gompertz-Makeham mortality model with varying parameters reveals complex patterns.

Keywords

• life disparity
• life table entropy
• remaining life expectancy
• variance in age at death