{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T11:46:06Z","timestamp":1773402366294,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,5,29]],"date-time":"2024-05-29T00:00:00Z","timestamp":1716940800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Graduate Studies and Scientific Research at Qassim University, Saudi Arabia"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, we consider the statistical analysis of the parameter estimation of the Marshall\u2013Olkin extended generalized extreme value under liner normalization distribution (MO-GEVL) within the context of progressively type-II censored data. The progressively type-II censored data are considered for three specific distribution patterns: fixed, discrete uniform, and binomial random removal. The challenge lies in the computation of maximum likelihood estimations (MLEs), as there is no straightforward analytical solution. The classical numerical methods are considered inadequate for solving the complex MLE equation system, leading to the necessity of employing artificial intelligence algorithms. This article utilizes the genetic algorithm (GA) to overcome this difficulty. This article considers parameter estimation through both maximum likelihood and Bayesian methods. For the MLE, the confidence intervals of the parameters are calculated using the Fisher information matrix. In the Bayesian estimation, the Lindley approximation is applied, considering LINEX loss functions and square error loss, suitable for both non-informative and informative contexts. The effectiveness and applicability of these proposed methods are demonstrated through numerical simulations and practical real-data examples.<\/jats:p>","DOI":"10.3390\/sym16060669","type":"journal-article","created":{"date-parts":[[2024,6,3]],"date-time":"2024-06-03T10:06:01Z","timestamp":1717409161000},"page":"669","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Estimation of Marshall\u2013Olkin Extended Generalized Extreme Value Distribution Parameters under Progressive Type-II Censoring by Using a Genetic Algorithm"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3246-1293","authenticated-orcid":false,"given":"Rasha Abd El-Wahab","family":"Attwa","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt"}]},{"given":"Shimaa Wasfy","family":"Sadk","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1466-8821","authenticated-orcid":false,"given":"Taha","family":"Radwan","sequence":"additional","affiliation":[{"name":"Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 52571, Saudi Arabia"},{"name":"Department of Mathematics and Statistics, Faculty of Management Technology and Information Systems, Port Said University, Port Said 42521, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s10614-006-9025-7","article-title":"An application of extreme value theory for measuring financial risk","volume":"27","author":"Gilli","year":"2006","journal-title":"Comput. 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