AN EFFICIENT FAMILY OF RATIO-CUM-PRODUCT ESTIMATORS FOR FINITE POPULATION MEAN IN SAMPLE SURVEYS

Abstract

This paper considers the problem of estimating the finite population mean $\bar{Y}$  of the study variable using information on two auxiliary variables $(x,z)$ . A family of ratio-cum-product estimators for population mean $\bar{Y}$  has been suggested. It has been shown that the usual unbiased estimator $\bar{y}$ , ratio estimator, product estimator, dual to ratio estimator and dual to product estimator due to Srivenkatramana (1980) and Bandyopadhyaya (1980), Singh et al's (2005, 2011) estimator, Tailor et al's (2012) estimator, Vishwakarma et al's (2014) estimator and  Vishwakarma and Kumar (2015) estimator are members of the suggested family of estimators. In addition to these estimators, various unknown estimators are shown to be the member of the suggested family of estimators. The bias and mean squared error of the proposed family are obtained under large sample approximation. Efficiency comparisons are made to demonstrate the performance of the suggested family over other existing estimators. An empirical study is carried out in support of the present study.

Keywords

• Auxiliary variables,Study variable,Ratio-cum-Product method of estimation,Bias,Mean Squared Error

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