This article addresses the problem of estimating the finite population mean using two auxiliary variables under two-stage sampling scheme. Further the proposed improved class of estimators are provided their genralized form. Mathematical properties of the existing and proposed improved generalized class of estimators are derived up to first order of approximation. We identified 11 members of the improved generalized class of estimators which are more efficient than existing estimators in terms of the percentage relative efficiency. We use two real data sets under two-stage sampling to compare the performances of all of considered estimators.

This paper addresses the issue of estimating the population mean for non-response using simple random sampling. A new family of estimators is proposed for estimating the population mean with auxiliary information on the sample mean and the rank of the auxiliary variable. Bias and mean square errors of existing and proposed estimators are obtained using the first order of measurement. Theoretical comparisons are made of the performance of the proposed and existing estimators. We show that the proposed family of estimators is more efficient than existing estimators in the literature under the given constraints using these theoretical comparisons.