Confidence intervals of mean residual life function in length-biased sampling based on modified empirical likelihood

The mean residual life (MRL) function is one of the basic parameters of interest in survival analysis. In this paper, we develop three procedures based on modified versions of empirical likelihood (EL) to construct confidence intervals of the MRL function with length-biased data. The asymptotic results corresponding to the procedures have been established. The proposed methods exhibit better finite sample performance over other existing procedures, especially in small sample sizes. Simulations are conducted to compare coverage probabilities and the mean lengths of confidence intervals under different scenarios for the proposed methods and some existing methods. Two real data applications are provided to illustrate the methods of constructing confidence intervals.