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Population Median Estimation Using Auxiliary Variables: A Simulation Study with Real Data Across Sample Sizes and Parameters

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  • Umer Daraz

    (School of Mathematics and Statistics, Central South University, Changsha 410017, China)

  • Fatimah A. Almulhim

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Mohammed Ahmed Alomair

    (Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia)

  • Abdullah Mohammed Alomair

    (Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia)

Abstract

This paper introduces an enhanced class of ratio estimators, which employ the transformation technique on an auxiliary variable under simple random sampling to estimate the population median. The transformation strategy can reduce both the bias and mean square error, which can help estimators become more efficient. The bias and mean square error of proposed estimators are investigated up to the first order of approximation. Through simulation studies and the analysis of various data sets, the performance of the proposed estimators is compared to existing methods. The proposed class of estimators improves the precision and efficiency of median estimation, ensuring more accurate and dependable results in various practical scenarios. The findings reveal that the new estimators show superior performance under the given conditions compared to traditional estimators.

Suggested Citation

  • Umer Daraz & Fatimah A. Almulhim & Mohammed Ahmed Alomair & Abdullah Mohammed Alomair, 2025. "Population Median Estimation Using Auxiliary Variables: A Simulation Study with Real Data Across Sample Sizes and Parameters," Mathematics, MDPI, vol. 13(10), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1660-:d:1659153
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    References listed on IDEAS

    as
    1. Muhammad Irfan & Maria Javed & Sandile C. Shongwe & Muhammad Zohaib & Sajjad Haider Bhatti, 2021. "Estimation of Population Median under Robust Measures of an Auxiliary Variable," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-14, September.
    2. Mir Subzar & Showkat Ahmad Lone & Emmanuel J Ekpenyong & Abdul Salam & Muhammad Aslam & T A Raja & Salmeh A Almutlak, 2023. "Efficient class of ratio cum median estimators for estimating the population median," PLOS ONE, Public Library of Science, vol. 18(2), pages 1-14, February.
    3. Umer Daraz & Mohammed Ahmed Alomair & Olayan Albalawi & Abdulaziz S. Al Naim, 2024. "New Techniques for Estimating Finite Population Variance Using Ranks of Auxiliary Variable in Two-Stage Sampling," Mathematics, MDPI, vol. 12(17), pages 1-14, September.
    4. Sibel Aladag & Hulya Cingi, 2015. "Improvement in Estimating the Population Median in Simple Random Sampling and Stratified Random Sampling Using Auxiliary Information," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(5), pages 1013-1032, March.
    5. Mohammed Ahmed Alomair & Umer Daraz, 2024. "Dual Transformation of Auxiliary Variables by Using Outliers in Stratified Random Sampling," Mathematics, MDPI, vol. 12(18), pages 1-16, September.
    6. Ramkrishna S. Solanki & Housila P. Singh, 2015. "Some Classes of Estimators for Median Estimation in Survey Sampling," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(7), pages 1450-1465, April.
    7. Javid Shabbir & Sat Gupta & Ghulam Narjis, 2022. "On improved class of difference type estimators for population median in survey sampling," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(10), pages 3334-3354, May.
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