An enhanced estimator of finite population variance using two auxiliary variables under simple random sampling

Sohaib Ahmad; Nitesh Kumar Adichwal; Muhammad Aamir; Javid Shabbir; Najwan Alsadat; Mohammed Elgarhy; Hijaz Ahmad

doi:10.1038/s41598-023-44169-5

An enhanced estimator of finite population variance using two auxiliary variables under simple random sampling

Sci Rep. 2023 Dec 5;13(1):21444. doi: 10.1038/s41598-023-44169-5.

Authors

Sohaib Ahmad¹, Nitesh Kumar Adichwal², Muhammad Aamir¹, Javid Shabbir³, Najwan Alsadat⁴, Mohammed Elgarhy⁵, Hijaz Ahmad^{6

7

8

9}

Affiliations

¹ Department of Statistics, Abdul Wali Khan University Mardan, Mardan, Pakistan.
² School of Business, University of Petroleum and Energy Studies, Dehradun, India. nnitesh139@gmail.com.
³ Department of Statistics, University of Wah at Wah Cant, Wah, Pakistan.
⁴ Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O.Box 71115, 11587, Riyadh, Saudi Arabia.
⁵ Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef, 62521, Egypt.
⁶ Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186, Rome, Italy.
⁷ Operational Research Center in Healthcare, Near East University, TRNC Mersin 10, 99138, Nicosia, Turkey.
⁸ Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, Mishref, Kuwait.
⁹ Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon.

Abstract

In this article, we have suggested a new improved estimator for estimation of finite population variance under simple random sampling. We use two auxiliary variables to improve the efficiency of estimator. The numerical expressions for the bias and mean square error are derived up to the first order approximation. To evaluate the efficiency of the new estimator, we conduct a numerical study using four real data sets and a simulation study. The result shows that the suggested estimator has a minimum mean square error and higher percentage relative efficiency as compared to all the existing estimators. These findings demonstrate the significance of our suggested estimator and highlight its potential applications in various fields. Theoretical and numerical analyses show that our suggested estimator outperforms all existing estimators in terms of efficiency. This demonstrates the practical value of incorporating auxiliary variables into the estimation process and the potential for future research in this area.