An efficient logarithmic estimator in stratified random sampling using single auxiliary variable

This paper proposes a novel logarithmic-type estimator for the estimation of the population mean under stratified random sampling when a single auxiliary variable is available. By employing a logarithmic transformation, the suggested estimator more effectively exploits auxiliary information, leading to improved estimation accuracy. Analytical expressions for the bias and precision of the estimator are derived, and theoretical conditions are established under which the proposed estimator dominates several existing estimators. The empirical performance is assessed using three real-life datasets, along with a simulation study based on three artificial populations of size 1000 generated from a normal distribution. Samples of sizes n = 50, 100, and 150 are drawn to evaluate estimator behavior under varying sampling intensities. The findings consistently show that the proposed estimator attains higher percentage relative efficiency and superior precision compared to competing estimators across both real and simulated datasets. These results demonstrate that the estimator offers substantial gains in survey accuracy, particularly when a strong association exists between the study and auxiliary variables.