Some estimator types for population mean using linear transformation with the help of the minimum and maximum values of the auxiliary variable

Abstract

Grover et al. [4] suggested two product type exponential estimators using linear transformation of auxiliary variable. This paper proposes ratio, product and product type exponential estimators of population mean using new three linear transformations. Transformations using the known minimum and maximum values of the auxiliary variable x have been considered. Theoretically, mean square errors (MSE) and biases equations of our proposed estimators are derived up to the first order approximation. The proposed estimators are more efficient than the classical ones under theoretical conditions. We obtain the superiority regions of the proposed product type exponential estimators. Additionally, we present the diagrams of these regions. A numerical example is perfomed to support the theoretical results.