{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T02:24:23Z","timestamp":1773368663970,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,7,25]],"date-time":"2025-07-25T00:00:00Z","timestamp":1753401600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU)","award":["IMSIU-DDRSP2502"],"award-info":[{"award-number":["IMSIU-DDRSP2502"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Accurate modeling of product lifetimes is vital in reliability analysis and engineering to ensure quality and maintain competitiveness. This paper proposes the progressively randomly censored Maxwell distribution, which incorporates both progressive Type-II and random censoring within the Maxwell distribution framework. The model allows for the planned removal of surviving units at specific stages of an experiment, accounting for both deliberate and random censoring events. It is assumed that survival and censoring times each follow a Maxwell distribution, though with distinct parameters. Both frequentist and Bayesian approaches are employed to estimate the model parameters. In the frequentist approach, maximum likelihood estimators and their corresponding confidence intervals are derived. In the Bayesian approach, Bayes estimators are obtained using an inverse gamma prior and evaluated through a Markov Chain Monte Carlo (MCMC) method under the squared error loss function (SELF). A Monte Carlo simulation study evaluates the performance of the proposed estimators. The practical relevance of the methodology is demonstrated using a real data set.<\/jats:p>","DOI":"10.3390\/axioms14080573","type":"journal-article","created":{"date-parts":[[2025,7,25]],"date-time":"2025-07-25T08:13:31Z","timestamp":1753431211000},"page":"573","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Bayesian Analysis of the Maxwell Distribution Under Progressively Type-II Random Censoring"],"prefix":"10.3390","volume":"14","author":[{"given":"Rajni","family":"Goel","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Physical Sciences, DIT University, Dehradun 248009, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5758-1035","authenticated-orcid":false,"given":"Mahmoud M.","family":"Abdelwahab","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7680-6762","authenticated-orcid":false,"given":"Mustafa M.","family":"Hasaballah","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, Marg Higher Institute of Engineering and Modern Technology, Cairo 11721, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,25]]},"reference":[{"key":"ref_1","unstructured":"Herd, G.R. 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