A Dual Auxiliary Variable Approach to Finite Population Variance Estimation

Hussain, Abid; Mukhtar, Rabbia; Masood, Muhammad Asim; Ali, Nasir

doi:10.22034/jirss.2026.2064841.1120

A Dual Auxiliary Variable Approach to Finite Population Variance Estimation

Document Type : Original Article

Authors

Abid Hussain

Rabbia Mukhtar

Muhammad Asim Masood

Nasir Ali

Department of Statistics, PMAS-Arid Agriculture University, Rawalpindi, Pakistan.

10.22034/jirss.2026.2064841.1120

Abstract

This study proposes a novel estimator for the finite population variance under simple random sampling. The estimator utilizes dual auxiliary information by incorporating the empirical cumulative distribution function (ECDF) of an auxiliary variable. The ECDF, which represents the stochastic process over the unit interval [0,1], is employed to enhance the estimation precision. The performance of the proposed estimator is evaluated through a comprehensive analysis. First, the bias and mean squared error (MSE) of the estimator are derived analytically. Second, a simulation study is conducted to investigate the estimator's behavior under various parametric settings. Finally, an empirical comparison is made with several well-established estimators using five real-world datasets. The results consistently demonstrate the superiority of the proposed estimator in terms of both bias and MSE, suggesting its practical utility.

Keywords

Auxiliary information

simple random sampling

mean squared error

empirical distribution function

simulation

Subjects

Sampling Methods

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