An improved generalized estimators for finite population variance of a study variable based on auxiliary information

Abstract

The information on auxiliary variable has been shown to be relevant in selection and estimation of parameters to gain more precision in estimates of study variable. The transformation of this auxiliary information also aids increase efficiency of estimators. In this article, an improved mixed ratio-product-type exponential estimator is proposed and evaluated using information on auxiliary variable for population variance under simple random sampling. The mathematical expressions for bias and mean squared error (MSE) of the proposed estimator were derived up to first order of approximation. Using real data sets and Monte Carlo simulation study, the performance evaluation of the proposed estimator was considered and compared to the existing estimators. The results of the empirical and simulation studies show that the proposed estimator outperformed the existing estimators in term of MSE and PRE.