Using Auxiliary Information and Their Ranks for Estimation of Finite Population Mean

Abstract

Survey statistician’s purpose has always been to produce the best estimates of unknown population parameters. In survey sampling, the selected sample might contain tied values. The idea of ranking with tied values takes the variation of the auxiliary variable into account. We have propose a two-fold application of auxiliary information in which auxiliary information is supported by original and ranked auxiliary variables. Simple and stratified random sampling schemes are used to establish mathematical developments. The results align perfectly with the idea of using auxiliary information to help estimate the required characteristics.We observe that using relevant information more thoroughly enhances the efficiency of the estimation process. Up to the first level of approximation, we formulate expressions for the bias and mean square errors of the proposed estimators. We conduct a theoretical assessment of the suggested estimators. We employed real-world data sets to demonstrate, through numerical analysis, how the proposed estimators perform, thus corroborating our theoretical conclusions. The analysis demonstrated that the proposed estimator performed better than the existing estimators