A New Family of Estimators for Population Mean with Dual Use of the Auxiliary Information

In this paper, a new family of estimators for the population mean is proposed using supplementary information on the mean and distribution function of the auxiliary variable. The expressions for the bias and mean square error of the proposed estimator are obtained under first order of approximation. The proposed estimator is compared with the existing estimators of the population mean (theoretically and numerically). A numerical study is conducted to examine the efficiencies of the existing and proposed estimators. It turns out that the proposed estimator is always more efficient than its existing counterparts in terms of percentage relative efficiency.