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

Wrycza, T. F.
Demographic Research, 30:50, 1405–1412 (2014)

## 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.
Das Max-Planck-Institut für demografische Forschung (MPIDR) in Rostock ist eines der international führenden Zentren für Bevölkerungswissenschaft. Es gehört zur Max-Planck-Gesellschaft, einer der weltweit renommiertesten Forschungsgemeinschaften.