Median augmented ranked set sampling for estimation of the population mean with applications to body health data

Zuhier Aldrabseh Mahmoud; Khudhayr A. Rashedi; Ali A. Atoom; Tariq S. Alshammari; Nesreen M. AL-Olaimat; Zuhier Aldrabseh Mahmoud; Khudhayr A. Rashedi; Ali A. Atoom; Tariq S. Alshammari; Nesreen M. AL-Olaimat

doi:10.3934/math.20251274

AIMS Mathematics

2025, Volume 10, Issue 12: 28954-28980. doi: 10.3934/math.20251274

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Median augmented ranked set sampling for estimation of the population mean with applications to body health data

1.
Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan
2.
Department of Mathematics, College of Science, University of Ha'il, Hail 55425, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Ajloun National University, Ajloun, Jordan
4.
Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajoun, Jordan

Received: 30 September 2025 Revised: 21 November 2025 Accepted: 28 November 2025 Published: 10 December 2025
MSC : 60E05, 62D05, 62F10

Ranked set sampling (RSS) is a sampling design that combines random sampling with the judgment of researchers through preliminary ranking. The current study introduced a new generalization of RSS, called median-augmented ranked set sampling (MARSS), designed to further reduce the measurement cost and lessen the influence of outliers in estimating the population mean. The proposed MARSS estimator was compared with both simple random sampling (SRS) and RSS estimators. Its exact relative precision and bias were evaluated for a range of symmetric and skewed distributions under perfect ranking. A simulation study was also conducted to assess its performance under imperfect ranking, when using concomitant variables, in the presence of outliers, and when considering ranking cost efficiency. The variance and robustness were also interpreted in topological space. The theoretical results showed that the MARSS estimator was unbiased for symmetric distributions and achieved less variance than both RSS and SRS in unimodal symmetric distributions. Overall, MARSS is more precise than SRS and surpassed RSS in most scenarios, though some bias was observed for skewed distributions. Importantly, MARSS demonstrated a greater robustness to outliers than either SRS or RSS. Finally, the new sampling design was illustrated through an application to body health data analysis.
- ranked set sampling,
- simple random sampling,
- estimation,
- perfect ranking,
- imperfect ranking,
- concomitant variables,
- ranking cost,
- topological space
Citation: Zuhier Aldrabseh Mahmoud, Khudhayr A. Rashedi, Ali A. Atoom, Tariq S. Alshammari, Nesreen M. AL-Olaimat. Median augmented ranked set sampling for estimation of the population mean with applications to body health data[J]. AIMS Mathematics, 2025, 10(12): 28954-28980. doi: 10.3934/math.20251274

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Abstract

Ranked set sampling (RSS) is a sampling design that combines random sampling with the judgment of researchers through preliminary ranking. The current study introduced a new generalization of RSS, called median-augmented ranked set sampling (MARSS), designed to further reduce the measurement cost and lessen the influence of outliers in estimating the population mean. The proposed MARSS estimator was compared with both simple random sampling (SRS) and RSS estimators. Its exact relative precision and bias were evaluated for a range of symmetric and skewed distributions under perfect ranking. A simulation study was also conducted to assess its performance under imperfect ranking, when using concomitant variables, in the presence of outliers, and when considering ranking cost efficiency. The variance and robustness were also interpreted in topological space. The theoretical results showed that the MARSS estimator was unbiased for symmetric distributions and achieved less variance than both RSS and SRS in unimodal symmetric distributions. Overall, MARSS is more precise than SRS and surpassed RSS in most scenarios, though some bias was observed for skewed distributions. Importantly, MARSS demonstrated a greater robustness to outliers than either SRS or RSS. Finally, the new sampling design was illustrated through an application to body health data analysis.

References

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