Outlier values and rankings are important for emphasizing data distribution variability, which improves the accuracy and effectiveness of variance estimations. To enhance the estimation of finite population variance in a two-phase sampling framework, this study presents an improved class of double exponential-type estimators by utilizing the outlier values and ranks of an auxiliary variable. A theoretical analysis is conducted to derive the biases and mean squared errors (MSEs) of these estimators using first-order approximations. A comprehensive simulation study is then performed to analyze the performance of the proposed estimators. The results clearly show that the new estimators provide more precise estimates, achieving a higher percentage relative efficiency (PRE) across all simulated scenarios. Furthermore, three data sets are analyzed to further confirm the efficiency of the proposed estimators as compared to other existing estimators. These results emphasize the potential of the proposed class of estimators to optimize variance estimation techniques, making it a more cost-effective and accurate choice for researchers using two-phase sampling in a variety of domains.

In this paper, we introduce a new, improved family of estimators aimed at improving the accuracy of finite population variance estimation. The proposed class of estimators is enhanced in terms of overall estimating performance and robustness by using the maximum and minimum values as supplementary information to improve precision and reliability. The bias and mean square error are theoretically obtained to the first order of approximation. We carried out a simulation study to evaluate the performance of the proposed estimators and validate the theoretical results. The findings show that the proposed estimators have higher percent relative efficiencies than the existing estimators across all of the simulated scenarios. Additionally, three independent symmetric and asymmetric datasets are analyzed to further confirm the better efficiency of proposed estimators compared with traditional estimators.