Efficient family of ratio-product type estimators of median

Abstract

For estimating the population median of the study variable using known information on population parameters based on auxiliary and study variables, a family of two parameter ratio-product type estimators has been proposed. The expressions for its bias and mean square error have been obtained up to first order of approximation. It has been shown that the efficiency of estimators can be increased with the appropriate choice of parameters. The conditions have been obtained under which proposed family of estimators is efficient than the conventional sample median, ratio and product type estimators of median defined by different authors. The expressions for the gain in efficiency of proposed family of estimators over the existing ones have also been obtained. The results obtained have also been illustrated numerically by taking data considered in literature.