Estimation of the Population Mean Based on Extremes Ranked Set Sampling

Abstract

This paper is concerned with ranked set sampling theory which is useful to estimate the population mean when the order of a sample of small size can be found without measurements or with other methods. In practice ranking a sample of moderate size and observing the i-th ranked unit (ranking of middle ordered units) is a difficult task. Therefore, in this paper we propose two estimators of the population mean based on extremes ranked set sampling methods. The proposed estimators are unbiased for the population mean when the underlying distribution is symmetric. It is shown that the proposed estimators are more efficient than their counter part simple random sampling method for distributions considered in this study.