{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T18:33:04Z","timestamp":1769193184633,"version":"3.49.0"},"reference-count":16,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,13]],"date-time":"2022-04-13T00:00:00Z","timestamp":1649808000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004663","name":"ministry of science and technology, Taiwan","doi-asserted-by":"publisher","award":["MOST 109-2118- M-032-001-MY2"],"award-info":[{"award-number":["MOST 109-2118- M-032-001-MY2"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Under progressive type II censoring, the credible interval estimation and the credible region for parameters of two-parameter exponential distribution based on the Bayesian approach are presented in this paper. Two methods of Bayesian credible region are proposed under a given confidence level. We also presented the predictive interval of the future observation under this type of censoring. In order to compare the performance of our proposed Bayesian credible interval and region with the existing non-Bayesian methods, we conduct a simulation study by the Monte Carlo method to find the corresponding coverage probabilities. This research is related to the topic of asymmetrical probability distributions and applications across disciplines. Finally, one engineering example is used to demonstrate the Bayesian credible interval estimation methods proposed in this paper.<\/jats:p>","DOI":"10.3390\/sym14040808","type":"journal-article","created":{"date-parts":[[2022,4,13]],"date-time":"2022-04-13T23:07:16Z","timestamp":1649891236000},"page":"808","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Interval Estimation for the Two-Parameter Exponential Distribution under Progressive Type II Censoring on the Bayesian Approach"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0611-6701","authenticated-orcid":false,"given":"Shu-Fei","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Statistics, Tamkang University, Tamsui, Taipei 251301, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Balakrishnan, N., and Aggarwala, R. (2000). Progressive Censoring: Theory, Methods, and Applications, Birkh\u00e4user.","DOI":"10.1007\/978-1-4612-1334-5"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1080\/00401706.1963.10490102","article-title":"Progressively censored samples in the life testing","volume":"5","author":"Cohen","year":"1963","journal-title":"Technometrics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1080\/00401706.1977.10489556","article-title":"Progressively censored sampling in the three parameter gamma distribution","volume":"19","author":"Cohen","year":"1977","journal-title":"Technometrics"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1007\/s11135-006-9008-8","article-title":"Interval Estimation for the Two-Parameter Exponential Distribution based on the Doubly Type II Censored Sample","volume":"41","author":"Wu","year":"2007","journal-title":"Qual. Quant."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wu, S.F. (2022). Bayesian interval estimation for the two-parameter exponential distribution based on the right type II censored sample. Symmetry, 14.","DOI":"10.3390\/sym14020352"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"113946","DOI":"10.1016\/j.enconman.2021.113946","article-title":"Bayesian infinite mixture models for wind speed distribution estimation","volume":"236","author":"Wang","year":"2021","journal-title":"Energy Convers. Manag."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"8205","DOI":"10.3934\/math.2021475","article-title":"Empirical E-Bayesian estimation for the parameter of Poisson distribution","volume":"6","author":"Mohammed","year":"2021","journal-title":"AIMS Math."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Heidari, K.F., Deiri, E., and Jamkhaneh, E.B. (2022). 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[2nd ed.]."},{"key":"ref_16","unstructured":"Lawless, J.F. (1982). Statistical Models and Methods for Lifetime Data, Wiley."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/4\/808\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:53:00Z","timestamp":1760136780000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/4\/808"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,13]]},"references-count":16,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["sym14040808"],"URL":"https:\/\/doi.org\/10.3390\/sym14040808","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,13]]}}}