An Enhanced the Efficiency of Ratio-cum-product Estimator for Estimating the Population Mean in the Sample Survey

This research aims to develop and propose a combined ratio and product estimator for accurately estimating the population mean in sample surveys. It leverages auxiliary variable information within the framework of simple random sampling without replacement. The proposed estimator is structured to encompass all previously studied related estimators. Additionally, the researcher analyzes key properties of the proposed estimator, including the mean squared error (MSE) and the minimum mean squared error.  The efficiency of the proposed estimator is assessed against other related estimators through theoretical analysis, real data applications, and data simulations, using relative efficiency as the evaluation criterion.   The findings reveal that, under identical study conditions, the proposed estimator exhibits superior efficiency compared to all other estimators examined in this study. These results are consistently observed across theoretical analyses, real data applications, and simulations.