Estimation of monotone α-quantile of past lifetime function with application

Abstract

In many physical situations, it is reasonable to assume that the α-quantile of past life functions is increasing. In this study, we propose a new estimator for an increasing α-quantile of the past life function for right-censored data. We investigate the asymptotic properties of the new estimator and explore its weak and strong convergence. The simulation results show that the new estimator is consistent and outperforms the usual estimator from the literature. As an illustrative example, a time event from a data set of the Mayo Clinic study on primary biliary cirrhosis was analyzed.

Keywords

• mathematical physics
• monotone quantile of past lifetime function
• right-censored data
• kaplan–meier survival estimator