Dual Transformation of Auxiliary Variables by Using Outliers in Stratified Random Sampling

To estimate the finite population variance of the study variable, this paper proposes an improved class of efficient estimators using different transformations. When both the minimum and maximum values of the auxiliary variable are known and the ranks of the auxiliary variable are associated with the study variable, these estimators are particularly useful. Therefore, the precision of the estimators can be effectively improved through the utilization of these rankings. We examine the properties of the proposed class of estimators, including bias and mean squared error (MSE), using a first-order approximation through a stratified random sampling method. To determine the performances and validate the findings mathematically, a simulation study is carried out. Based on the results, the proposed class of estimators performs better in terms of the mean squared error $\left(MSE\right)$ and percent relative efficiency $\left(PRE\right)$ as compared to other estimators in all scenarios. Furthermore, in order to prove that the performances of the improved class of estimators are better than those of the existing estimators, three data sets are examined in the application section.