Table of Contents
Advances in Statistics
Volume 2014, Article ID 974604, 9 pages
Research Article

Efficient Estimators Using Auxiliary Variable under Second Order Approximation in Simple Random Sampling and Two-Phase Sampling

Department of Statistics, Banaras Hindu University, Varanasi 221005, India

Received 21 July 2014; Accepted 19 August 2014; Published 3 September 2014

Academic Editor: Chin-Shang Li

Copyright © 2014 Rajesh Singh and Prayas Sharma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper suggests some estimators for population mean of the study variable in simple random sampling and two-phase sampling using information on an auxiliary variable under second order approximation. Bahl and Tuteja (1991) and Singh et al. (2008) proposed some efficient estimators and studied the properties of the estimators to the first order of approximation. In this paper, we have tried to find out the second order biases and mean square errors of these estimators using information on auxiliary variable based on simple random sampling and two-phase sampling. Finally, an empirical study is carried out to judge the merits of the estimators over others under first and second order of approximation.