A generalised family of ratio product estimator using transformation equation

TL;DR

This paper proposes a generalized family of ratio and product estimators for population variance estimation using transformations and auxiliary information, with theoretical analysis and empirical validation.

Contribution

It introduces a new family of estimators based on transformations for variance estimation, improving upon existing methods.

Findings

The proposed estimators have lower mean square error than traditional estimators.

Theoretical expressions for bias and MSE are derived up to first order.

Empirical results demonstrate the effectiveness of the new estimators.

Abstract

In this paper we deal with the estimation of population variance of the study variable y using auxiliary information on variable x. A family of ratio and product-type estimators are proposed using suitable transformation on both random variable x(auxiliary variable) and(study variable).Up to the first order of approximation the expression of mean square error and Bias term are obtained. An empirical study is carried out to illustrate the performance of the constructed estimator over others.