Ratio type exponential estimators of population mean under linear transformation of auxiliary variable : theory and methods

In the present paper, two ratio type exponential estimators of population mean have been proposed by making use of the transformed auxiliary variates. Here, the transformed auxiliary variates are obtained under the assumption that the extreme values of the original auxiliary variate in the population are known in advance. The biases and mean square errors of these proposed estimators have been obtained, up to first order of approximation. A comparative study of the proposed estimators with some of the existing estimators, with respect to their biases and mean square errors, has been carried out. The overall preference regions of all the estimators considered in the paper have been obtained and have been represented diagrammatically. A numerical illustration has been taken to support the theoretical results obtained in the paper.