Abstract / Summary
The use of auxiliary information is a long-standing technique in survey sampling to improve the precision of estimating population parameters. If auxiliary variables are highly correlated with the study variable, then the sample mean from an SRSWOR is typically not the best estimator. The literature presents several estimators based on a single auxiliary variable, such as ratio, product, regression, and exponential forms. In more recent years, the interdependence of several sources of auxiliary information has become of great interest due to the potential for additional gains in efficiency. A generalized exponential-type estimator of the finite population mean is derived by combining an auxiliary variable and its rank information with the help of (SRSWOR). The bias and mean squared error (MSE) of the suggested estimator are analytically computed, and the optimal values of the unknown constants are found using a first-order approximation. The theoretical and empirical results based on four real populations demonstrate the superiority of the proposed estimator over all competing estimators. The proposed estimator consistently yields the minimum MSE and maximum percent relative efficiency (PRE) for Populations I, II, III, and IV, respectively, of 676.08%, 190.40%, 118.90%, and 4843.70%. In particular, the great improvement seen with Population IV indicates the success of the fusion of auxiliary and rank information. The results validate the proposed estimator for estimating finite population mean and show it to be a realistic and highly efficient method.