{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T08:30:38Z","timestamp":1761294638002,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,10]],"date-time":"2023-08-10T00:00:00Z","timestamp":1691625600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71661012"],"award-info":[{"award-number":["71661012"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper investigates the problem of entropy estimation for the generalized Rayleigh distribution under progressively type-II censored samples. Based on progressively type-II censored samples, we first discuss the maximum likelihood estimation and interval estimation of Shannon entropy for the generalized Rayleigh distribution. Then, we explore the Bayesian estimation problem of entropy under three types of loss functions: K-loss function, weighted squared error loss function, and precautionary loss function. Due to the complexity of Bayesian estimation computation, we use the Lindley approximation and MCMC method for calculating Bayesian estimates. Finally, using a Monte Carlo statistical simulation, we compare the mean square errors to examine the superiority of maximum likelihood estimation and Bayesian estimation under different loss functions. An actual example is provided to verify the feasibility and practicality of various estimations.<\/jats:p>","DOI":"10.3390\/axioms12080776","type":"journal-article","created":{"date-parts":[[2023,8,10]],"date-time":"2023-08-10T10:52:40Z","timestamp":1691664760000},"page":"776","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Estimation of Entropy for Generalized Rayleigh Distribution under Progressively Type-II Censored Samples"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2460-2845","authenticated-orcid":false,"given":"Haiping","family":"Ren","sequence":"first","affiliation":[{"name":"Teaching Department of Basic Subjects, Jiangxi University of Science and Technology, Nanchang 330013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qin","family":"Gong","sequence":"additional","affiliation":[{"name":"College of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xue","family":"Hu","sequence":"additional","affiliation":[{"name":"College of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.csda.2004.05.008","article-title":"Generalized Rayleigh distribution: Different methods of estimations","volume":"49","author":"Kundu","year":"2005","journal-title":"Comput. 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