{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T09:58:58Z","timestamp":1782381538048,"version":"3.54.5"},"reference-count":14,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T00:00:00Z","timestamp":1751846400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"American University of Sharjah (AUS)","award":["FRG22-C-S60\/AS1624"],"award-info":[{"award-number":["FRG22-C-S60\/AS1624"]}]},{"name":"AUS Faculty research grant","award":["FRG22-C-S60\/AS1624"],"award-info":[{"award-number":["FRG22-C-S60\/AS1624"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Outlier detection plays a key role in data analysis by improving data quality, uncovering data entry errors, and spotting unusual patterns, such as fraudulent activities. Choosing the right detection method is essential, as some approaches may be too complex or ineffective depending on the data distribution. In this study, we explore a simple yet powerful approach using the range distribution to identify outliers in univariate data. We compare the effectiveness of two range statistics: we normalize the range by the standard deviation (\u03c3) and the interquartile range (IQR) across different types of distributions, including normal, logistic, Laplace, and Weibull distributions, with varying sample sizes (n) and error rates (\u03b1). An evaluation of the range behavior across multiple distributions allows for the determination of threshold values for identifying potential outliers. Through extensive experimental work, the accuracy of both statistics in detecting outliers under various contamination strategies, sample sizes, and error rates (\u03b1=0.1,0.05,0.01) is investigated. The results demonstrate the flexibility of the proposed statistic, as it adapts well to different underlying distributions and maintains robust detection performance under a variety of conditions. Our findings underscore the value of an adaptive method for reliable anomaly detection in diverse data environments.<\/jats:p>","DOI":"10.3390\/e27070731","type":"journal-article","created":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T10:03:27Z","timestamp":1751882607000},"page":"731","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Empirical Evaluation of the Relative Range for Detecting Outliers"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-1794-3397","authenticated-orcid":false,"given":"Dania","family":"Dallah","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, American University of Sharjah, Sharjah 26666, United Arab Emirates"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4952-8298","authenticated-orcid":false,"given":"Hana","family":"Sulieman","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, American University of Sharjah, Sharjah 26666, United Arab Emirates"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8282-3921","authenticated-orcid":false,"given":"Ayman Al","family":"Zaatreh","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, American University of Sharjah, Sharjah 26666, United Arab Emirates"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3946-0920","authenticated-orcid":false,"given":"Firuz","family":"Kamalov","sequence":"additional","affiliation":[{"name":"School of Engineering, Applied Science and Technology, Canadian University Dubai, Dubai 14143, United Arab Emirates"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"375","DOI":"10.3390\/geotechnics3020022","article-title":"Review of applicable outlier detection methods to treat geomechanical data","volume":"3","author":"Dastjerdy","year":"2023","journal-title":"Geotechnics"},{"key":"ref_2","first-page":"447","article-title":"A Review and Empirical Comparison of Univariate Outlier Detection Methods","volume":"37","author":"Saleem","year":"2021","journal-title":"Pak. J. Statist."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Massi, M., Ieva, F., and Lettieri, E. (2020). Data mining application to healthcare fraud detection: A two-step unsupervised clustering method for outlier detection with administrative databases. BMC Med. Inform. Decis. Mak., 20.","DOI":"10.1186\/s12911-020-01143-9"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Malini, N., and Pushpa, M. (2017, January 27\u201328). Analysis on credit card fraud identification techniques based on KNN and outlier detection. Proceedings of the 2017 Third International Conference on Advances in Electrical, Electronics, Information, Communication and Bio-Informatics (AEEICB), Chennai, India.","DOI":"10.1109\/AEEICB.2017.7972424"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.accinf.2016.04.001","article-title":"Outlier detection in healthcare fraud: A case study in the Medicaid dental domain","volume":"21","author":"Capelleveen","year":"2016","journal-title":"Int. J. Account. Inf. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Chakhchoukh, Y., Liu, S., Sugiyama, M., and Ishii, H. (2016, January 17\u201321). Statistical outlier detection for diagnosis of cyber attacks in power state estimation. Proceedings of the 2016 IEEE Power And Energy Society General Meeting (PESGM), Boston, MA, USA.","DOI":"10.1109\/PESGM.2016.7741572"},{"key":"ref_7","unstructured":"Tukey, J. (1977). Exploratory Data Analysis, Addison-Wesley Pub. 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Math."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/7\/731\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:05:58Z","timestamp":1760033158000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/7\/731"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,7]]},"references-count":14,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7]]}},"alternative-id":["e27070731"],"URL":"https:\/\/doi.org\/10.3390\/e27070731","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,7]]}}}