Model Assisted Statistics and Applications 6 (2011) 47–55 47 DOI 10.3233/MAS-2011-0163 IOS Press An improved estimator of the finite population mean in simple random sampling Lovleen Kumar Grover ∗ and Paramdeep Kaur Department of Mathematics, Guru Nanak Dev University, Punjab, India Abstract. When the population mean of an auxiliary variable is known in advance then the use of various ratio type, product type and regression type estimators is widely acceptable in the literature of survey sampling for estimating the population mean of a study variable. Under the same situations, here we propose a new exponential type estimator of the finite population mean of a study variable. The expressions for the bias and mean square error of the proposed estimator have been obtained. It has been shown that the proposed estimator is always better than most of the existing estimators. To support theoretical results obtained, we have considered a numerical illustration. Keywords: Auxiliary variable, bias, efficiency, mean square error, simple random sampling, study variable 1. Introduction, notations and various existing estimators It is well established phenomenon in the theory of sample surveys that the auxiliary information is often used to improve the accuracy of estimators of unknown population parameters. The use of auxiliary information at the estimation stage appears to have started with the work of Watson [38] and Cochran [5]. Let y and x denote the study variable and the auxiliary variable respectively, which are correlated with each other. Let ¯ Y and ¯ X denote the unknown population mean of variable y and known population mean of variable x respectively. Consider a simple random sample (without replacement) of size n drawn from the given finite population of size N . Let (¯ y, ¯ x) denote the sample means of the bivariate (y,x). When ¯ X is known in advance then for estimating ¯ Y , (i) Watson [38] suggested the usual regression estimator, ¯ y lr =¯ y + b ( ¯ X - ¯ x ) , where b is the regression coefficient of y on x in the sample, (ii) Cochran [5] introduced the usual ratio estimator, ¯ y R =¯ y ¯ X ¯ x , (iii) Robson [20] and Murthy [12] gave the usual product estimator, ¯ y P =¯ y ¯ x ¯ X . It is well known that the estimators ¯ y R and ¯ y P are preferred over the mean per unit estimator ¯ y if the variables y and x are respectively highly positively and highly negatively correlated with each other. It has been theoretically established that, in general, the regression estimator is more efficient than the usual ratio and product estimators except when the regression line of y on x passes through the neighborhood of the origin, in which case the efficiencies of these estimators are almost equal. We are mentioning below some of the generalizations of these estimators carried out by a number of authors. ∗ Corresponding author: Lovleen Kumar Grover, Department of Mathematics, Guru Nanak Dev University, Amritsar-143 005, Punjab, India. E-mail: lovleen 2@yahoo.co.in. ISSN 1574-1699/11/$27.50  2011 – IOS Press and the authors. All rights reserved