A modified ratio-product estimator of population mean using some known parameters of the auxiliary variable

Abstract

The estimation of population mean is one of the challenging aspects in sampling theory and population study and much effort has been vigorously employed to improve the precision of estimates. In this research work, a modified ratio-product estimator of population mean Y of the study variable Y using median and coefficient of variation of the auxiliary variabl X , in simple random sampling scheme is proposed. The expression of bias and MSE of the proposed estimator have been obtained under large sample approximation, asymptotically optimum estimator (AOE) is identified with its approximate MSE formula. Estimator based on “estimated optimum values” was also investigated. Theoretical and empirical comparison of proposed estimator with some other ratio and product estimators justified the performance of the proposed estimators. A minimum of 20 percent reduction in the MSE were observed from each of the existing estimators considered. It is found that the proposed estimator were uniformly better than all other modified ratio and product estimators and thus most preferred over the existing estimators for the use in practical application.

Keywords: Finite population mean, bias, mean square error, auxiliary variable, optimum estimator, study variable