{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T22:37:08Z","timestamp":1777502228274,"version":"3.51.4"},"reference-count":36,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,20]],"date-time":"2025-07-20T00:00:00Z","timestamp":1752969600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Saud University, Riyadh, Saudi Arabia","award":["ORF-2025-538"],"award-info":[{"award-number":["ORF-2025-538"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper presents a comprehensive statistical analysis of the Gumbel Type-II distribution based on joint progressive Type-II censoring. It derives the maximum likelihood estimators for the distribution parameters and constructs their asymptotic confidence intervals. It investigates Bayesian estimation using non-informative and informative priors under the squared error loss function and the LINEX loss function, applying Markov Chain Monte Carlo methods. A detailed simulation study evaluates the estimators\u2019 performance in terms of average estimates, mean squared errors, and average confidence interval lengths. Results show that Bayesian estimators can outperform maximum likelihood estimators, especially with informative priors. A real data example demonstrates the practical use of the proposed methods. The analysis confirms that the Gumbel Type-II distribution with joint progressive censoring provides a flexible and effective model for lifetime data, enabling more accurate reliability assessment and risk analysis in engineering and survival studies.<\/jats:p>","DOI":"10.3390\/axioms14070544","type":"journal-article","created":{"date-parts":[[2025,7,21]],"date-time":"2025-07-21T09:33:53Z","timestamp":1753090433000},"page":"544","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On Joint Progressively Censored Gumbel Type-II Distributions: (Non-) Bayesian Estimation with an Application to Physical Data"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7680-6762","authenticated-orcid":false,"given":"Mustafa M.","family":"Hasaballah","sequence":"first","affiliation":[{"name":"Department of Basic Sciences, Marg Higher Institute of Engineering and Modern Technology, Cairo 11721, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3493-033X","authenticated-orcid":false,"given":"Mahmoud E.","family":"Bakr","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8870-9692","authenticated-orcid":false,"given":"Oluwafemi Samson","family":"Balogun","sequence":"additional","affiliation":[{"name":"Department of Computing, University of Eastern Finland, FI-70211 Kuopio, Finland"}]},{"given":"Arwa M.","family":"Alshangiti","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gumbel, E. (1958). Statistics of Extremes, Columbia University Press.","DOI":"10.7312\/gumb92958"},{"key":"ref_2","first-page":"65","article-title":"Bayesian estimation, prediction and characterization for the Gumbel model based on records","volume":"36","author":"Mousa","year":"2002","journal-title":"Stat. J. Theor. Appl. 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