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Mathematical Problems in Engineering
Volume 2014, Article ID 937397, 5 pages
Research Article

An Efficient Estimation of the Mean Residual Life Function with Length-Biased Right-Censored Data

1School of Mathematics, Shandong University, Jinan, Shandong 250100, China
2College of Science, China University of Petroleum, Qingdao 266580, China

Received 20 March 2014; Accepted 26 May 2014; Published 9 June 2014

Academic Editor: Jian Guo Zhou

Copyright © 2014 Hongping Wu and Yihui Luan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The mean residual life (MRL) function for a lifetime random variable is one of the basic parameters of interest in survival analysis. In this paper, we propose a new estimator of the MRL function with length-biased right-censored data and evaluate its performance through a small Monte Carlo simulation study. The results of the simulations show that the proposed estimator outperforms the existing one referred to in Data and Model Setup Section in terms of Monte Carlo bias and mean square error, especially when the censoring rate is heavy. We also show that the proposed estimator converges in distribution under some conditions.