A General Family of Estimators for Estimating Population Mean Using Known Value of Some Population Parameter(s)

TL;DR

This paper introduces a versatile family of estimators for population mean that leverage known population parameters, deriving bias and MSE expressions, and demonstrating their effectiveness through empirical analysis.

Contribution

It proposes a new general family of estimators for population mean that encompasses existing estimators as special cases, with derived bias and MSE formulas.

Findings

The estimators' bias and MSE are derived up to first order.

Some existing estimators are shown as special cases of the proposed family.

Empirical results demonstrate the proposed estimators' improved performance.

Abstract

A general family of estimators for estimating the population mean of the variable under study, which make use of known value of certain population parameter(s), is proposed. Under Simple Random Sampling Without Replacement (SRSWOR) scheme, the expressions of bias and mean-squared error (MSE) up to first order of approximation are derived. Some well known estimators have been shown as particular member of this family. An empirical study is carried out to illustrate the performance of the constructed estimator over others.