A Theoretical Inference About Ratio Estimation of Population Mean Using Ranked Set Sampling Under Bivariate Normal Distribution

Abstract

Ranked set sampling is a sampling technique that uses ranking information when measuring units is difficult or expensive. In this study, ratio estimation of the population mean is considered in the case of units ranking by both auxiliary variable and the variable of interest in ranked set sampling under bivariate normal distribution. We obtained some theoretical inferences about the mean square error of the ratio estimation in this situation in a simple form depending on coefficient of variation. Besides, we made a theoretical comparison of mean square errors by ranking based on auxiliary variable and interested variable. Using this comparison, one can choose which ranking strategy should be utilized by using correlation coefficient and coefficients of variation of interested variable and auxiliary variable in a problem easily. When the coefficients of variation are close to each other and the correlation coefficient is close to one, ranking can be conducted according to any variable. However, when the coefficient of variation of the interested variable is greater than the coefficient of variation of the auxiliary variable and the correlation coefficient between them is small, ranking should be preferred by using the interested variable. The performance of the ratio estimators was compared by a simulation study. The simulation results indicated that the ranked set sampling estimators were more efficient than the simple random sampling estimators for the same sample size and correlation coefficient. A real data example was also given to demonstrate for calculating relative efficiencies.