Robust Ratio- and Product-Type Estimators Under Non-normality via Linear Transformation Using Certain Known Population Parameters

Abstract

In the literature, a linear transformation on an auxiliary variable has been widely used to increase the efficiencies of ratio- and product-type estimators. However, additional information of unknown population parameters is required to utilize such estimators. In this paper, we propose two novel ratio-type and two novel product-type estimators under non-normality using the minimum and maximum values of the auxiliary variable. The expressions for mean square errors and biases for the proposed estimators are derived. We also calculate confidence intervals of the estimators. Theoretical results are supported using simulation studies. We also illustrate our results using a real life application of a body fat data set. We study robustness properties of the proposed estimators. We show that the proposed ratio-type estimators which utilize certain known auxiliary information can improve some other existing estimators which do not utilize such auxiliary information.