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

Umer Daraz, Fatimah A. Almulhim, Mohammed Ahmed Alomair () and Abdullah Mohammed Alomair
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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

Mathematics, 2025, vol. 13, issue 10, 1-18

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.

Keywords: auxiliary information; population median; robust and non-conventional measures; sample sizes; skewed distributions; simulation study; bias; percent relative efficiency (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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