Estimation of a Biometric Function

In the analysis of life tables one biometric function of interest is the life expectancy at age x, eₓ = E X - x X > x. Estimation of eₓ is considered, the standard estimator used in life tables is shown to be asymptotically unbiased, uniformly strong consistent, and converges in distribution to a Gaussian process. The connections of the estimator studied in this article and that used in reliability theory are illustrated.