Classes of Dual to Modified Ratio Estimators for Estimating Population Mean in Simple Random Sampling

Abstract

This paper proposes two new classes of dual to modified ratio estimators for estimating population mean when information on a known auxiliary variable is available, and was inspired by Jaroengeratikun and Lawson (2019) and uses the transformation of auxiliary variables technique under simple random sampling without replacement. The general expressions of the bias and mean square errors (MSEs) of the proposed classes of estimators up to the first order of approximation have been obtained. The performance of the proposed classes of estimators are compared with existing estimators using a theoretical approach, a simulation study, and an application to real data. In the simulation study and practical application, the percentage relative efficiency (PREs) of all estimators with respect to the usual ratio estimator are used to compare the performance of the proposed class of estimators. The proposed classes of dual to modified ratio estimators are found to be more efficient than the existing estimators in the estimation of the population mean under a certain given condition.