{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:27:22Z","timestamp":1760059642906,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T00:00:00Z","timestamp":1750896000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia","award":["PNURSP2025R745"],"award-info":[{"award-number":["PNURSP2025R745"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper discusses the Bayesian estimation for the unknown parameters, reliability and hazard rate functions of the doubly truncated Zubair-Weibull distribution. Informative priors (gamma distribution) for the parameters are used to obtain the posterior distributions. Under the squared-error and linear\u2013exponential loss functions, the Bayes estimators are derived. Credible intervals for the parameters, reliability and hazard rate functions are obtained. Bayesian prediction (point and interval) for the future observation is considered under the two-sample prediction scheme. A simulation study is performed using the Markov Chain Monte Carlo algorithm of simulation for different sample sizes to assess the performance of the estimators. Two real datasets are applied to show the flexibility and applicability of the distribution.<\/jats:p>","DOI":"10.3390\/axioms14070502","type":"journal-article","created":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T03:33:25Z","timestamp":1750995205000},"page":"502","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Bayesian Analysis of the Doubly Truncated Zubair-Weibull Distribution: Parameter Estimation, Reliability, Hazard Rate and Prediction"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7040-5623","authenticated-orcid":false,"given":"Zakiah I.","family":"Kalantan","sequence":"first","affiliation":[{"name":"Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}]},{"given":"Mai A.","family":"Hegazy","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls\u2019 Branch), Tafahna Al-Ashraf, Cairo 11751, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3247-2013","authenticated-orcid":false,"given":"Abeer A.","family":"EL-Helbawy","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls\u2019 Branch), Tafahna Al-Ashraf, Cairo 11751, Egypt"},{"name":"Higher Institute of Marketing, Commerce & Information Systems (MCI), Cairo 11511, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7017-8336","authenticated-orcid":false,"given":"Hebatalla H.","family":"Mohammad","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"given":"Doaa S. A.","family":"Soliman","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls\u2019 Branch), Tafahna Al-Ashraf, Cairo 11751, Egypt"}]},{"given":"Gannat R.","family":"AL-Dayian","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls\u2019 Branch), Tafahna Al-Ashraf, Cairo 11751, Egypt"}]},{"given":"Mervat K.","family":"Abd Elaal","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls\u2019 Branch), Tafahna Al-Ashraf, Cairo 11751, Egypt"},{"name":"Canal High Institute of Engineering and Technology, Suez 43511, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1007\/BF00050852","article-title":"Relationships for moments of order statistics from the right-truncated generalized half logistic distribution","volume":"48","author":"Balakrishnan","year":"1996","journal-title":"Ann. 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