SOME NEW FUNCTIONAL FORMS OF THE RATIO AND THE PRODUCT ESTIMATORS OF THE POPULATION MEAN

Abstract

In this paper, some new functional forms of ratio and product estimators of population mean, namely, logarithmic ratio and product estimators have been introduced. The expressions of biases and mean square errors (MSEs) of these estimators have been obtained up to order . Further, the proposed estimators have been compared with the mean per unit, usual ratio and product estimators, and it has been found that the former are more efficient than the latter under a certain set of conditions. Also, under some practical situations, biases of proposed estimators are less than the corresponding biases of exponential ratio and product type estimators. Moreover, to improve the efficiency of proposed estimators, the transformation have been considered by shifting the origin of auxiliary variable and the optimum transformations have also been found for the proposed estimators for which MSEs of these estimators become minimum.