A Generalized Estimation Strategy for the Finite Population Median Using Transformation Methods Under a Two-Phase Sampling Design

This paper introduces an efficient improved class of estimators for the finite population median under a two-phase sampling scheme. The proposed estimators are developed using transformation techniques to improve the estimation precision over that of conventional approaches. Two-phase sampling is employed to reduce data collection costs and enhance estimation accuracy, especially when complete auxiliary information is not easily available. Expressions for the bias and mean squared error (MSE) are derived using a first-order approximation. To assess performance, simulation studies were carried out using data generated from various statistical distributions, alongside several real-life datasets. Estimators are compared using the mean squared error criterion, and the results show that the proposed methods consistently outperform the existing ones in terms of accuracy and efficiency. Graphical comparisons further support the improved performance of the new estimators, highlighting their practical effectiveness in median estimation problems.