An Efficient New Ratio-Type and Ratio-Type Exponential Estimator for Population Mean in Sample Surveys

Abstract

This paper addresses the problem of estimating the finite population mean of the study variable using information on auxiliary variable in sample surveys. A class of ratio-type and ratio-type exponential formulae for estimating finite population mean is defined. The bias and mean squared error of the proposed class of estimators are obtained up to terms of order n⁻¹ under simple random sampling without replacement (SRSWOR) sampling scheme. The optimum conditions are obtained at which the mean squared error is minimum. It has been shown theoretically that at the optimum conditions, the proposed class of estimators is more efficient than the customary unbiased estimator, ratio and regression estimators. We have also obtained the condition in which the proposed class of estimators is superior to Rao’s (1991) estimator. Two numerical exemplifications are given in support of the present study.

Keywords: Population Mean; Bias; Mean squared error; Ratio-type exponential estimator.

2010 Mathematics Subject Classification. 26A25; 26A35