The cross-sectional distribution of completed lifetimes: Some new inferences from survival analysis

The cross-sectional distribution of completed lifetimes (DCL) is a new estimator defined and derived by Dixon (2012) in the general Taylor price model (GTE). DCL can be known as the cross-sectional weighted estimator summing to 1. It is a new statistics applying to describe the data. This paper focuses on the cross-sectional distribution in the survival analysis. The delta method is applied to derive the variance of the of three cumulative distribution functions: the distribution of duration, cross-sectional distribution of age, distribution of duration across rms. The Monte Carlo experiment is applied to do the simulation study. The empirical results show that the asymptotic variance formula of the DCL and distribution of duration performs well when the sample size above 25. With the increasing of the sample size, the bias of the variance is reduced.