Ranked set sampling in the presence of censored data

Abstract

The ranked set sampling (RSS) technique has been shown to be superior to classical simple random sampling (SRS) in the sense that it always provides a more precise estimator of the population mean. However, it is quite often that some measurements are below the limit of detection and hence become censored. In such situations, the superiority of RSS over SRS may no longer be held. In this article we consider the problem of estimating the population mean and standard deviation based on a ranked set sample with some data being censored. Maximum likelihood estimators are proposed when the data are assumed to follow a lognormal distribution. In the case where the distribution is unknown, a variant of the Kaplan-Meier estimator is proposed in the estimation of the population mean. A simulation study is conducted to compare the performance of the proposed RSS estimators with the corresponding SRS estimators. The impact of imperfect judgment ranking is also discussed. The proposed methods are applied to a real data set on mercury concentration in swordfish. Copyright © 2002 John Wiley & Sons, Ltd.