{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T17:50:57Z","timestamp":1767117057421,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T00:00:00Z","timestamp":1632700800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004054","name":"King Abdulaziz University","doi-asserted-by":"publisher","award":["KEP \u2013 PhD - 69 - 130 - 42"],"award-info":[{"award-number":["KEP \u2013 PhD - 69 - 130 - 42"]}],"id":[{"id":"10.13039\/501100004054","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Dynamic cumulative residual (DCR) entropy is a valuable randomness metric that may be used in survival analysis. The Bayesian estimator of the DCR R\u00e9nyi entropy (DCRR\u00e9E) for the Lindley distribution using the gamma prior is discussed in this article. Using a number of selective loss functions, the Bayesian estimator and the Bayesian credible interval are calculated. In order to compare the theoretical results, a Monte Carlo simulation experiment is proposed. Generally, we note that for a small true value of the DCRR\u00e9E, the Bayesian estimates under the linear exponential loss function are favorable compared to the others based on this simulation study. Furthermore, for large true values of the DCRR\u00e9E, the Bayesian estimate under the precautionary loss function is more suitable than the others. The Bayesian estimates of the DCRR\u00e9E work well when increasing the sample size. Real-world data is evaluated for further clarification, allowing the theoretical results to be validated.<\/jats:p>","DOI":"10.3390\/e23101256","type":"journal-article","created":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T10:39:20Z","timestamp":1632739160000},"page":"1256","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Bayesian Analysis of Dynamic Cumulative Residual Entropy for Lindley Distribution"],"prefix":"10.3390","volume":"23","author":[{"given":"Abdullah M.","family":"Almarashi","sequence":"first","affiliation":[{"name":"Statistics Department, Faculty of Science, King Abdulaziz University, Jeddah 21551, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ali","family":"Algarni","sequence":"additional","affiliation":[{"name":"Statistics Department, Faculty of Science, King Abdulaziz University, Jeddah 21551, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amal S.","family":"Hassan","sequence":"additional","affiliation":[{"name":"Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2236-4935","authenticated-orcid":false,"given":"Ahmed N.","family":"Zaky","sequence":"additional","affiliation":[{"name":"Institute of National Planning, Cairo 11765, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1333-3862","authenticated-orcid":false,"given":"Mohammed","family":"Elgarhy","sequence":"additional","affiliation":[{"name":"The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra, Algarbia 31951, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,27]]},"reference":[{"key":"ref_1","first-page":"547","article-title":"On measures of Entropy and Information","volume":"1","year":"1961","journal-title":"Proceeding of the Fourth Berkeley Symposium on Mathematical Statistics and Probability"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1103\/PhysRevA.72.012332","article-title":"An information-theoretic security proof for quantum-key-distribution protocols","volume":"72","author":"Renner","year":"2005","journal-title":"Phys. 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