Optimal approach to enhancing population mean estimation using auxiliary parameters

This study presents an efficient method for estimating the population mean of a study variable using a Searls exponential ratio estimator. The approach is based on simple random sampling and leverages known population parameters of an auxiliary variable for enhanced estimation of population mean. Using large sample approximations up to the first order, the expressions for the bias and mean squared error of the proposed estimator are derived. To evaluate its performance, the estimator is compared conceptually and mathematically with several existing estimators. Theoretical results are further validated through both simulated and real-world data sets. Findings from these evaluations demonstrate that the proposed estimator consistently outperforms many competing estimators, particularly at higher population mean values. Therefore, it holds promise for improving population mean estimation across a range of practical applications.