Hybrid Estimators for Finite Population Variance: Combining Auxiliary Data with Traditional Methods

This study introduces three innovative hybrid efficient estimators designed for estimating population variance within the framework of simple random sampling. It highlights the critical role of auxiliary variables and their corresponding measures in the formulation of these hybrid estimators. We derive the bias and mean squared error of the proposed estimators, applying up to the first order of approximation. Additionally, we calculate the percent relative efficiency of these estimators and assess their performance against several established estimators using both gamma-simulated and real data sets. The results demonstrate that our proposed estimators typically achieve a lower mean squared error compared to the usual unbiased estimator and other existing estimators under specified conditions.