Ratio estimation of the population mean using auxiliary information in simple random sampling and median ranked set sampling

Abstract

In this article, two modified ratio estimators of the population mean are suggested provided that the first or third quartiles of the auxiliary variable can be established when the mean of the auxiliary variable is known. The double-sampling method is used to estimate the mean of the auxiliary variable if it is unknown. The suggested estimators are investigated under simple random sampling (SRS) and median ranked set sampling (MRSS) schemes. The new estimators when using MRSS are compared to their counterparts under SRS. The bias and the mean square error of the proposed estimators are derived. It turns out that the estimators are approximately unbiased and the MRSS estimators are more efficient than the SRS estimators, on the basis of the same sample size, correlation coefficient, and quartile. A real data set is used for illustration.