Estimation of population mean using auxiliary information: A simulation approach

Abstract

In this paper, different existing ratio estimators using one auxiliary variable are reviewed and their efficiencies are compared with known correlation coefficient. A bivariate population was generated using R software. Simple random sampling without replacement method was used for the selection of sample from the generated population. The different ratio estimators were compared with respect to bias, mean square error, skewness and kurtosis using simulation technique. Efficiencies of the estimators were compared and it is found that in comparison with traditional ratio estimator, all the estimators viz. E1, E2, E3, E4, E5, E6, E7, E8, E9 and E10 were more efficient whereas E11 and E12 were less efficient for all the studied sample sizes and correlation coefficients. It was observed that as sample size increase then bias and mean square error both decreases within each correlation coefficient between X and Y. All the estimators were almost unbiased for both the populations for large sample size.