Use of Coefficient of Skewness and Quartile Deviation of Auxiliary Variable for Improved Estimation of Population Mean

The present manuscript is about the improved estimation of population mean of the main variable (y) under study using ratio type estimator by making a suitable use of the coefficient of variation and the quartile deviation of the auxiliary variable (x) through well known kappa technique. The mathematical expressions for the bias and mean squared error (MSE) of the proposed estimator up to the first order of approximation have been obtained. The optimum value of the constant kappa (κ ) has been obtained by minimizing the mean squared error of the proposed estimator. The optimum estimator is also obtained for the optimum value of the constant kappa and its optimum properties are also studied. Finally an empirical study is also carried out for the justification of the theoretical findings and it has been shown that the proposed estimator is better than the mentioned estimators of the population mean as it has lesser mean squared error among the mentioned estimators of population mean.