Product type exponential estimators of population mean under linear transformation of auxiliary variable in simple random sampling

This paper proposes two product type exponential estimators of population mean of study variable using linear transformation of auxiliary variable with the assumption that the extreme values (i.e. maximum and minimum values) of auxiliary variable in the population are known in advance. The expressions for biases and mean square errors of proposed estimators are obtained, up to first order of approximation. Theoretical conditions have been made under which our proposed estimators are superior to the existing ones. The overall preference regions of all the estimators considered in this paper are constructed and represented them diagrammatically. A numerical illustration is considered to support and verify the superiority of our proposed estimators. (C) 2012 Elsevier Inc. All rights reserved.