Generalized Class of Estimators for Population Variance Using Information on Two Auxiliary Variables

Abstract

Yasmeen et al. (Int J Appl Comput Math 1(2), 1–10, 2015) introduced an exponential ratio cum dual to ratio type of estimator for the population mean and compared the performance of the several estimators using the derived expression of MSE. But unfortunately, the expressions of bias and MSE of their proposed estimator \(\hbox {t}_{\mathrm{n}/2\mathrm{G}}\) is found to be incorrect and hence the comparison based on incorrect MSE, carried by them, is wrong. In the present article, the author provides the correct expressions of the bias and MSE of estimator proposed by Yasmeen et al. (Int J Appl Comput Math 1(2), 1–10, 2015), up to the first order of approximation and an attempt is made to provide an estimate for the population variance \(\hbox {S}_{\mathrm{y}}^2\) of the study variable y under SRWOR using information on two auxiliary variables x and z. Bias and MSE expressions have been derived up to the first order of approximation. An empirical study is carried out in the support of theoretical results.