Improved Estimation Of Mean Under Ranked Set Sampling Using Auxiliary Information

Abstract

This paper aims to introduce a new approach to efficient mean estimators under ranked set sampling. In cases where the ranks of the auxiliary variables exhibit a positive correlation with the primary research variable, the proposed estimators are derived from a linear combination of conventional estimators such as product, ratio, and exponential. As performance metrics, the estimators' Mean Square Error (MSE) and Bias are utilized to assess their effectiveness. In addition to deriving the theoretical properties of the suggested estimators, the conditions under which they perform better than the current estimators are examined. Additionally, real data sets are used to empirically evaluate the proposed estimators, and the findings show that, under ranked set sampling, the suggested estimators consistently produce the best results under all circumstances. A data-driven simulation study demonstrates that the proposed estimators outperform the current estimators covered in the literature.