Generalized Estimators for Finite Population Variance Using Measurable and Affordable Auxiliary Character

Abstract

In this paper, a generalized exponential-type estimator for estimating the population variance using measurable and affordable auxiliary character in single phase sampling has been proposed. Some special cases of the proposed generalized estimator with a = 1 and a = 2 have also been discussed. The expressions for the mean square error and bias of the proposed generalized estimator have been derived. The efficiency of the proposed generalized estimator has been compared theoretically with the existing estimators and the conditions under which the proposed estimators are better than some existing estimators have also been given.  Numerical examples with five real data sets to compute MSEs and PREs were conducted to ascertain the efficiency of the proposed estimators over others and the results showed that both of the proposed estimators were more efficient than the estimators considered in literature. Thus, the estimator with  perform better than the estimator with a = 1.