Simulation-Based Evaluation of Robust Transformation Techniques for Median Estimation Under Simple Random Sampling
An efficient estimator can reduce both bias and mean squared error to provide more accurate results by using the transformation strategy. In this paper, an enhanced class of ratio–product types of estimators is introduced, which employs the transformation technique by linearly combining two robust m...
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MDPI AG
2025-04-01
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| author | Fatimah A. Almulhim Abdulaziz S. Alghamdi |
| author_facet | Fatimah A. Almulhim Abdulaziz S. Alghamdi |
| author_sort | Fatimah A. Almulhim |
| collection | DOAJ |
| description | An efficient estimator can reduce both bias and mean squared error to provide more accurate results by using the transformation strategy. In this paper, an enhanced class of ratio–product types of estimators is introduced, which employs the transformation technique by linearly combining two robust measures, the trimean and decile mean, and five non-conventional measures, the range, inter-quartile range, mid-range, quartile average, and quartile deviation, on auxiliary variables with a simple random sampling method to estimate the finite population median. This transformation approach improves efficiency and enables estimators to manage data variability better. Using these estimators, we investigate their bias and mean squared error up to the first order of approximation. A comparison of the proposed estimators and existing methods is conducted through five simulated populations generated through different suitable distributions and three real datasets. By improving the precision and efficiency of median estimation, the proposed estimators ensure accurate and reliable results. Comparing the new estimators to traditional estimators, the findings show superior performance for new estimators in terms of mean squared errors (MSEs). |
| format | Article |
| id | doaj-art-1d71bcf5a8134d6eb86a776ea7ab847e |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
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| spelling | doaj-art-1d71bcf5a8134d6eb86a776ea7ab847e2025-08-20T02:24:42ZengMDPI AGAxioms2075-16802025-04-0114430110.3390/axioms14040301Simulation-Based Evaluation of Robust Transformation Techniques for Median Estimation Under Simple Random SamplingFatimah A. Almulhim0Abdulaziz S. Alghamdi1Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematics, College of Science & Arts, King Abdulaziz University, P.O. Box 344, Rabigh 21911, Saudi ArabiaAn efficient estimator can reduce both bias and mean squared error to provide more accurate results by using the transformation strategy. In this paper, an enhanced class of ratio–product types of estimators is introduced, which employs the transformation technique by linearly combining two robust measures, the trimean and decile mean, and five non-conventional measures, the range, inter-quartile range, mid-range, quartile average, and quartile deviation, on auxiliary variables with a simple random sampling method to estimate the finite population median. This transformation approach improves efficiency and enables estimators to manage data variability better. Using these estimators, we investigate their bias and mean squared error up to the first order of approximation. A comparison of the proposed estimators and existing methods is conducted through five simulated populations generated through different suitable distributions and three real datasets. By improving the precision and efficiency of median estimation, the proposed estimators ensure accurate and reliable results. Comparing the new estimators to traditional estimators, the findings show superior performance for new estimators in terms of mean squared errors (MSEs).https://www.mdpi.com/2075-1680/14/4/301simple random samplingauxiliary informationrobust measuresbiasmean squared errors |
| spellingShingle | Fatimah A. Almulhim Abdulaziz S. Alghamdi Simulation-Based Evaluation of Robust Transformation Techniques for Median Estimation Under Simple Random Sampling Axioms simple random sampling auxiliary information robust measures bias mean squared errors |
| title | Simulation-Based Evaluation of Robust Transformation Techniques for Median Estimation Under Simple Random Sampling |
| title_full | Simulation-Based Evaluation of Robust Transformation Techniques for Median Estimation Under Simple Random Sampling |
| title_fullStr | Simulation-Based Evaluation of Robust Transformation Techniques for Median Estimation Under Simple Random Sampling |
| title_full_unstemmed | Simulation-Based Evaluation of Robust Transformation Techniques for Median Estimation Under Simple Random Sampling |
| title_short | Simulation-Based Evaluation of Robust Transformation Techniques for Median Estimation Under Simple Random Sampling |
| title_sort | simulation based evaluation of robust transformation techniques for median estimation under simple random sampling |
| topic | simple random sampling auxiliary information robust measures bias mean squared errors |
| url | https://www.mdpi.com/2075-1680/14/4/301 |
| work_keys_str_mv | AT fatimahaalmulhim simulationbasedevaluationofrobusttransformationtechniquesformedianestimationundersimplerandomsampling AT abdulazizsalghamdi simulationbasedevaluationofrobusttransformationtechniquesformedianestimationundersimplerandomsampling |