{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T03:22:47Z","timestamp":1775704967966,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,18]],"date-time":"2025-03-18T00:00:00Z","timestamp":1742256000000},"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","award":["IMSIU-DDRSP2503"],"award-info":[{"award-number":["IMSIU-DDRSP2503"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This article introduces a new continuous lifetime distribution within the Gamma family, called the induced Xgamma distribution, and explores its various statistical properties. The proposed distribution\u2019s estimation and prediction are investigated using Bayesian and non-Bayesian approaches under progressively Type-II censored data. The maximum likelihood and maximum product spacing methods are applied for the non-Bayesian approach, and some of their performances are evaluated. In the Bayesian framework, the numerical approximation technique utilizing the Metropolis\u2013Hastings algorithm within the Markov chain Monte Carlo is employed under different loss functions, including the squared error loss, general entropy, and LINEX loss. Interval estimation methods, such as asymptotic confidence intervals, log-normal asymptotic confidence intervals, and highest posterior density intervals, are also developed. A comprehensive numerical study using Monte Carlo simulations is conducted to evaluate the performance of the proposed point and interval estimation methods through progressive Type-II censored data. Furthermore, the applicability and effectiveness of the proposed distribution are demonstrated through three real-world datasets from the fields of medicine and engineering.<\/jats:p>","DOI":"10.3390\/sym17030457","type":"journal-article","created":{"date-parts":[[2025,3,18]],"date-time":"2025-03-18T11:02:31Z","timestamp":1742295751000},"page":"457","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Estimation and Bayesian Prediction for New Version of Xgamma Distribution Under Progressive Type-II Censoring"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8303-1782","authenticated-orcid":false,"given":"Ahmed R.","family":"El-Saeed","sequence":"first","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\/0000-0001-8076-1544","authenticated-orcid":false,"given":"Molay Kumar","family":"Ruidas","sequence":"additional","affiliation":[{"name":"Department of Statistics, Trivenidevi Bhalotia College, Raniganj 713347, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8938-9187","authenticated-orcid":false,"given":"Ahlam H.","family":"Tolba","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Balakrishnan, N., and Aggarwala, R. 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