{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T03:46:59Z","timestamp":1769226419786,"version":"3.49.0"},"reference-count":20,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,26]],"date-time":"2022-09-26T00:00:00Z","timestamp":1664150400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This study presents a new three-parameter beta distribution defined on the unit interval, which can have increasing, decreasing, left-skewed, right-skewed, approximately symmetric, bathtub, and upside-down bathtub shaped densities, and increasing, U, and bathtub shaped hazard rates. This model can define well-known distributions with various parameters and supports, such as Kumaraswamy, beta exponential, exponential, exponentiated exponential, uniform, the generalized beta of the first kind, and beta power distributions. We present a comprehensive account of the mathematical features of the new model. Maximum likelihood methods and a Bayesian method under squared error and linear exponential loss functions are presented; also, approximate confidence intervals are obtained. We present a simulation study to compare all the results. Two real-world data sets are analyzed to demonstrate the utility and adaptability of the proposed model.<\/jats:p>","DOI":"10.3390\/axioms11100504","type":"journal-article","created":{"date-parts":[[2022,9,27]],"date-time":"2022-09-27T21:23:27Z","timestamp":1664313807000},"page":"504","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["A New 3-Parameter Bounded Beta Distribution: Properties, Estimation, and Applications"],"prefix":"10.3390","volume":"11","author":[{"given":"Faiza A.","family":"Althubyani","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, Taibah University, Al-Madina 41411, Saudi Arabia"}]},{"given":"Ahmed M. T.","family":"Abd El-Bar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Taibah University, Al-Madina 41411, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2196-8312","authenticated-orcid":false,"given":"Mohamad A.","family":"Fawzy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Taibah University, Al-Madina 41411, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Suez University, Suez 43111, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6767-4016","authenticated-orcid":false,"given":"Ahmed M.","family":"Gemeay","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,26]]},"reference":[{"key":"ref_1","unstructured":"Johnson, N.L., Kemp, A.W., and Balakrishnan, N. (1995). Continuous Univariate Distributions, Wiley. [2nd ed.]."},{"key":"ref_2","unstructured":"Johnson, N.L., Kotz, S., and Balakrisnan, N. (1994). Continuous Univariate Distributions, Wiley. [2nd ed.]."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1111\/j.1475-4991.2007.00220.x","article-title":"Estimating income inequality in China using grouped data and the generalized beta distribution","volume":"Volume 53","author":"Chotikapanich","year":"2007","journal-title":"Review of Income and Wealth"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Ng, D.W.W., Koh, S.K., Sim, S.Z., and Lee, M.C. (2019). The study of properties in generalized beta distribution. IOP Conf. Series J. 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