Estimation of Population Mean by Using a Generalized Family of Estimators Under Classical Ranked Set Sampling

Estimation of population mean of study variable Y suffers loss of precision in the presence of high variation in the data set. The use of auxiliary information incorporated in construction of an estimator under Rank set sampling scheme results in efficient estimation of population mean. In this paper, we propose an efficient generalized family of estimators to estimate finite population mean of study variable under ranked set sampling utilizing information on an auxiliary variable. Bias and Mean Square Error (MSE) of the proposed generalized family of estimators are derived. The conditions of efficiency of proposed generalized family of estimators from competitor estimators are also derived. The applications of estimator are discussed using simulation study and real-life data sets for comparisons of efficiency. It is concluded that when correlation between study and auxiliary variables increases, the proposed generalized family of estimators proves to be the efficient estimator of population mean of the study variable.