Quantiles of the conditional residual lifetime

Abstract

The study of the residual lifetime received considerable attention in survival analysis and in other disciplines like reliability theory and actuarial science. The quantile residual lifetime function, the inverse of the residual lifetime distribution P(T-1 - t(1) <= y vertical bar T-1 > t(1)), provides an interesting and well-studied measure to analyse residual lifetimes. In this paper we generalize the residual lifetime distribution and the quantile residual lifetime function by adding an extra conditioning of the form {T-2 <= t(2)} or {T-2 > t(2)}, where T-2 is a second variable containing extra information on T-1. Wepropose, for right-censored lifetimes, nonparametric estimators for this generalized conditional remaining lifetime distribution and the corresponding quantile function and we derive the asymptotic theory. In a simulation study, we show the good performance of the newly proposed quantile estimators and we discuss an application to real data on primary biliary cirrhosis.