Some efficient exponential estimators in survey sampling: A simulation study

In the framework of sampling theory, a factor-type exponential ratio estimator is proposed for the estimation of the population mean.  The estimator takes into account a spectrum of alpha values (constants) spanning $-1$ to $+1$ when analysing supplementary information for the study variable.  The study demonstrates the effectiveness of the suggested estimators by deriving bias and mean square error equations up to the first degree of large sample approximation.  The analysis shows that the proposed estimators perform better than the existing exponential estimators taken into account throughout this study, indicating noticeably lower mean squared errors.  The article also evaluates the suggested estimator's % relative efficiency when compared to the usual mean estimator.  The work demonstrates the superior performance of the suggested estimators over their exponential counterparts through numerical demonstration and simulation analysis, demonstrating an improvement in estimation efficiency.  The purpose of this study is to improve the efficiency of survey sample estimators by utilizing auxiliary information.  Simulation studies were used to develop and evaluate new exponential estimators, with an emphasis on bias, mean squared error (MSE), and relative efficiency as compared to established approaches.  The results revealed that the proposed estimators had decreased bias and MSE, resulting in significant efficiency gains, especially when the auxiliary variables were significantly linked with the principal variable of interest.  These findings demonstrate the novel estimators' adaptability and practical applicability, making them an important tool for accurate and efficient population parameter estimation in survey sampling.