{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:47:23Z","timestamp":1760147243305,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T00:00:00Z","timestamp":1674086400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004826","name":"Beijing Natural Science Foundation","doi-asserted-by":"publisher","award":["Z210003"],"award-info":[{"award-number":["Z210003"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Outliers often occur during data collection, which could impact the result seriously and lead to a large inference error; therefore, it is important to detect outliers before data analysis. Gamma distribution is a popular distribution in statistics; this paper proposes a method for detecting multiple upper outliers from gamma (m,\u03b8). For computing the critical value of the test statistic in our method, we derive the density function for the case of a single outlier and design two algorithms based on the Monte Carlo and the kernel density estimation for the case of multiple upper outliers. A simulation study shows that the test statistic proposed in this paper outperforms some common test statistics. Finally, we propose an improved testing method to reduce the impact of the swamping effect, which is demonstrated by real data analyses.<\/jats:p>","DOI":"10.3390\/axioms12020107","type":"journal-article","created":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T05:50:20Z","timestamp":1674107420000},"page":"107","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Method for Detecting Outliers from the Gamma Distribution"],"prefix":"10.3390","volume":"12","author":[{"given":"Xiou","family":"Liao","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Capital Normal University, Beijing 100048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tongtong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Capital Normal University, Beijing 100048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guohua","family":"Zou","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Capital Normal University, Beijing 100048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,19]]},"reference":[{"key":"ref_1","unstructured":"Barnett, V., and Lewis, T. 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Stat."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1080\/03610920902783856","article-title":"Detecting outliers in gamma distribution","volume":"39","author":"Nooghabi","year":"2010","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1081\/STA-120018552","article-title":"A new statistic for detecting outliers in exponential case","volume":"32","author":"Zerbet","year":"2003","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1323","DOI":"10.1080\/02664763.2011.645158","article-title":"Multiple outlier test for upper outliers in an exponential sample","volume":"39","author":"Lalitha","year":"2012","journal-title":"J. Appl. 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Math."},{"key":"ref_16","first-page":"263","article-title":"On the use and interpretation of certain test criteria for purposes of statistical inference: Part II","volume":"20A","author":"Neyman","year":"1928","journal-title":"Biometrika"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1007\/s11633-020-1243-2","article-title":"Study on statistical outlier detection and labelling","volume":"17","year":"2020","journal-title":"Int. J. Autom. 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