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...

Full description

Saved in:
Bibliographic Details
Main Authors: Fatimah A. Almulhim, Abdulaziz S. Alghamdi
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Axioms
Subjects:
Online Access:https://www.mdpi.com/2075-1680/14/4/301
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850156088233558016
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
record_format Article
series Axioms
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