Enhanced exponential ratio-cum-ratio estimator in ranked set sampling using transformed auxiliary information

Abstract

Estimation of population mean is a determined subject issue in sampling surveys and many efforts have been paid by various researchers to enhance the precision of the estimates by utilizing the correlated auxiliary information. In connection with this, we suggest an improved exponential ratio-cum-ratio estimator using transformed auxiliary variables under ranked set sampling scheme. Theoretical comparison between estimators is made in terms of mean square errors ($MSEs$), percentage relative efficiencies ($PREs$), and percentage relative root mean squared error ($PRRMSE$). The numerical expression for the bias and $MSE$ of the suggested estimator is derived up to first order of approximation. Based on the results of actual data sets and a simulation study, it is found that the suggested estimator perform well as compared to its existing counterparts.

Keywords: Exponential estimator; MSE; PRE; Ratio estimator; Transformed auxiliary variables.