{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T00:08:54Z","timestamp":1778544534414,"version":"3.51.4"},"reference-count":42,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,12]],"date-time":"2022-11-12T00:00:00Z","timestamp":1668211200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007414","name":"Deputyship for Research and Innovation, Ministry of Education, Saudi Arabia","doi-asserted-by":"publisher","award":["QU-IF-05-04-27802"],"award-info":[{"award-number":["QU-IF-05-04-27802"]}],"id":[{"id":"10.13039\/501100007414","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Censored data play a pivotal role in life testing experiments since they significantly reduce cost and testing time. Hence, this paper investigates the problem of statistical inference for a system of progressive first-failure censoring data for a new Weibull\u2013Pareto distribution. Maximum likelihood estimates for the parameters as well as some lifetime indices such as reliability, hazard rate functions, and coefficient of variation are derived. Lindley approximation and the Markov chain Monte Carlo technique are applied to obtain the Bayes estimates relative to two different loss functions: balanced linear exponential and general entropy loss functions. The results of the Bayes estimate are computed under the consideration of informative prior function. A real-life example \"the survival times in years of a group of patients given chemotherapy treatment\" is presented to illustrate the proposed methods. Finally, a simulation study is carried out to determine the performance of the maximum likelihood and Bayes estimates and compare the performance of different corresponding confidence intervals.<\/jats:p>","DOI":"10.3390\/sym14112395","type":"journal-article","created":{"date-parts":[[2022,11,14]],"date-time":"2022-11-14T02:34:58Z","timestamp":1668393298000},"page":"2395","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["General Entropy with Bayes Techniques under Lindley and MCMC for Estimating the New Weibull\u2013Pareto Parameters: Theory and Application"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5619-210X","authenticated-orcid":false,"given":"Mohamed S.","family":"Eliwa","sequence":"first","affiliation":[{"name":"Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia"},{"name":"Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy"},{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7828-3536","authenticated-orcid":false,"given":"Rashad M.","family":"EL-Sagheer","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science, Al-Azhar University, Naser City 11884, Egypt"},{"name":"High Institute of Computer and Management Information System, First Statement, New Cairo 11865, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Samah H.","family":"El-Essawy","sequence":"additional","affiliation":[{"name":"Astronomy Department, National Research Institute of Astronomy and Geophysics, Helwan 11421, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bader","family":"Almohaimeed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraydah 51482, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5402-8960","authenticated-orcid":false,"given":"Fahad S.","family":"Alshammari","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7585-5519","authenticated-orcid":false,"given":"Mahmoud","family":"El-Morshedy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"},{"name":"Department of Statistics and Computer Sciences, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1547","DOI":"10.1016\/j.csda.2010.01.003","article-title":"Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data","volume":"54","author":"Kundu","year":"2010","journal-title":"Comput. 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