ON THE DISTRIBUTION OF EMPIRICAL LIFE TABLE FUNCTIONS

John J. Hsieh (U.S.A.) and Cheng C. Chen (U.S.A.)

Received May 5, 2009

Abstract

This article develops statistical inference on life table functions. It is an application of the distributional properties of empirical generalized survival functions of Hsieh [9]. We first define the empirical life table functions from the conventional life table functions (see Hsieh [8]) and then study their distributional properties. We then derive therefrom the functions of biometric importance and obtain the Markov and martingale properties of the basic counting processes. We derive the means, variances and covariances as well as the asymptotic distributions of the empirical life table functions. Finally, we establish the weak convergence of the empirical survival function process and life expectancy process to Brownian bridge which enables statistical comparisons of life table functions to be made using newly derived variance formulas of the empirical functions.

Keywords and phrases: life table functions, empirical functions, asymptotic variance functions, empirical processes, weak convergence, Brownian bridge.