Modified Ratio-Cum-Product Estimators for Estimation of Population Mean Using Two Auxilliary Variables

Abstract

The estimation of population parameters, particularly the mean, is a challenging issue in most fields of human endeavor nowadays. The present paper introduces a new modified ratio-cum-product estimator for the estimation of the population mean, which utilizes information from two auxiliary variables together with population parameters, namely the sample size and the population’s correlation coefficients between the survey and auxiliary variables. The expressions for the bias and the mean squared error for the proposed estimator were derived up to the first order of approximations. To check on the performance of the proposed estimator, a theoretical efficiency comparison between the proposed and the other estimators was carried out. The theoretical efficiency comparison shows that the proposed estimator is better than the other estimators subject to some stated conditions. An empirical study was conducted to further compare the proposed estimator with other estimators numerically. Data from some populations were used to compute the mean squared errors and the Percentage relative efficiencies (PRE) for both the proposed and the considered estimators. The performance of the estimators was judged on the basis of the computed results. It was found that the mean squared error of the proposed estimator was minimum compared to that of the other estimators and the result from the PRE shows a considerable gain in efficiency. Hence, the proposed estimator outperforms the other estimators considered for comparison, and it will, therefore, be considered as the most efficient estimator. Thus, the proposed estimator can be used in practical scenarios and is, therefore, recommended.