Estimation of Population Mean Using Estimator Based on Auxiliary Variable in Simple Random Sampling

Abstract

Survey sampling is a well-established methodology employed to choose a sample of individuals from a larger population. The primary objective of this study is to estimate the population mean efficiently, by employing a comprehensive approach. To achieve this, we proposed a generalized estimator up to first degree of approximation by use of one auxiliary variable under simple random sampling framework. By deriving expressions for both bias and mean square error (MSE) of the proposed generalized estimator, we are able to ascertain its effectiveness. Remarkably, our analysis reveals that the proposed generalized estimator outperforms. Furthermore, we obtained the minimum MSE of the proposed estimator, and empirical studies demonstrated that our estimator outperform than the existing estimator found in the literature in terms of efficiency. Finally it is shown that the proposed generalized estimator efficiently work.