{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T22:13:43Z","timestamp":1767910423791,"version":"3.49.0"},"reference-count":31,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,14]],"date-time":"2024-06-14T00:00:00Z","timestamp":1718323200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Faisal University, Saudi Arabia","award":["6059"],"award-info":[{"award-number":["6059"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>A flexible distribution has been introduced to handle random variables in the unit interval. This distribution is based on an exponential transformation of the truncated positive normal distribution with two parameters and can effectively fit data with varying degrees of skewness and kurtosis. Therefore, it presents an alternative for modeling this type of data. Several mathematical and statistical properties of this distribution have been derived, such as moments, hazard function, the Bonferroni curve, and entropy. Moreover, we investigate the characterizations of the proposed distribution based on its hazard function. Parameter estimation has been performed using both the maximum likelihood method and method of the moments. Because of this, we were able to determine the best critical region and the information matrix, facilitating the calculation of asymptotic confidence intervals. A simulation study is presented to analyze the behavior of the obtained estimators for different sample sizes. To demonstrate the suitability of the proposed distribution, applications and goodness-of-fit tests have been performed on two practical data sets.<\/jats:p>","DOI":"10.3390\/axioms13060397","type":"journal-article","created":{"date-parts":[[2024,6,14]],"date-time":"2024-06-14T03:52:53Z","timestamp":1718337173000},"page":"397","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Statistical Advancement of a Flexible Unitary Distribution and Its Applications"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7302-7461","authenticated-orcid":false,"given":"Hugo S.","family":"Salinas","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ingenier\u00eda, Universidad de Atacama, Copiap\u00f3 1531772, Chile"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3189-0670","authenticated-orcid":false,"given":"Hassan S.","family":"Bakouch","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Tanta University, Tanta 31111, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8047-6882","authenticated-orcid":false,"given":"Fatimah E.","family":"Almuhayfith","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, King Faisal University, Alahsa 31982, Saudi Arabia"}]},{"given":"Wilson E.","family":"Caimanque","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ingenier\u00eda, Universidad de Atacama, Copiap\u00f3 1531772, Chile"}]},{"given":"Leonardo","family":"Barrios-Blanco","sequence":"additional","affiliation":[{"name":"Doctorado en Did\u00e1ctica de la Matem\u00e1tica, Facultad de Ciencias B\u00e1sicas, Universidad Cat\u00f3lica del Maule, Talca 3480112, Chile"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7772-0386","authenticated-orcid":false,"given":"Olayan","family":"Albalawi","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Science, University of Tabuk, Tabuk 47512, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/s11766-018-3354-x","article-title":"Inference for a truncated positive normal distribution","volume":"33","author":"Olmos","year":"2018","journal-title":"Appl. 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