• ### An Efficient Dual to Ratio and Product Estimator of Population Variance in Sample Surveys

Subhash Kumar Yadav, Sheela Misra, Ravendra Kumar, Shailendra Verma, Shailendra Kumar

Abstract: The present manuscript deals with the estimation of population variance using auxiliary variable. Here we proposed an efficient dual to ratio and product type estimator of population variance of study variable utilizing auxiliary information in the form of coefficient of kurtosis and the population mean of the auxiliary variable. To the first order of approximations, the bias and the mean squared error of the proposed variance have been obtained. The optimum value of the characterizing scalar has been obtained. This optimum value of characterizing scalar minimizes the mean squared error of the proposed estimator. The minimum value of the mean squared error has been obtained for this optimum value of the characterizing scalar. A comparison of the proposed estimator has been made with the mentioned existing estimators of population variance. Through an empirical study, the performances of different estimators of population variance are judged by calculating mean squared errors of different estimators. It has been seen that the proposed estimators has minimum mean squared error among all mentioned estimators.

Keywords: Main variable, auxiliary variable, bias, mean squared error, efficiency.