Use of an efficient unbiased estimator for finite population mean.

In this study, we propose an improved unbiased estimator in estimating the finite population mean using a single auxiliary variable and rank of the auxiliary variable by adopting the Hartley-Ross procedure when some parameters of the auxiliary variable are known. Expressions for the bias and mean square error or variance of the estimators are obtained up to the first order of approximation. Four real data sets are used to observe the performances of the estimators and to support the theoretical findings. It turns out that the proposed unbiased estimator outperforms as compared to all other considered estimators. It is also observed that using conventional measures have significant contributions in achieving the efficiency of the estimators.