Enhanced Exponential Type Ratio Estimator for Estimating Population Mean in Stratified Random Sampling under Linear Cost Function

This study focuses on calculating the population mean using stratified random sampling with an auxiliary variable provided. To minimize mean square error (MSE) and maximize percentage relative efficiency (PRE), the suggested estimator’s MSE is assessed using a linear cost function. A theoretical comparison is made with existing estimators to determine the criteria required for enhanced performance. The best allocation corresponding to the proposed estimator’s MSE is calculated utilizing an integer programming approach combined with the Lagrange multiplier technique. The estimator’s performance is further tested by comparing it to existing approaches on both real-world and simulated datasets. The results show that the suggested estimator regularly beats current alternatives in terms of efficiency.