{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,21]],"date-time":"2025-11-21T12:21:18Z","timestamp":1763727678391,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,3,9]],"date-time":"2020-03-09T00:00:00Z","timestamp":1583712000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, we introduced a new extension of the binomial-exponential 2 distribution. We discussed some of its structural mathematical properties. A simple type Copula-based construction is also presented to construct the bivariate- and multivariate-type distributions. We estimated the model parameters via the maximum likelihood method. Finally, we illustrated the importance of the new model by the study of two real data applications to show the flexibility and potentiality of the new model in modeling skewed and symmetric data sets.<\/jats:p>","DOI":"10.3390\/sym12030440","type":"journal-article","created":{"date-parts":[[2020,3,13]],"date-time":"2020-03-13T08:58:59Z","timestamp":1584089939000},"page":"440","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["A New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data"],"prefix":"10.3390","volume":"12","author":[{"given":"Abdulhakim","family":"A. Al-babtain","sequence":"first","affiliation":[{"name":"Department of Statistics and Operations Research, King Saud University, Riyadh 11362, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"I.","family":"Elbatal","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science Imam Muhammad ibn Saud Islamic University, Riyadh 11432, Saudi Arabia"},{"name":"Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Benha 13513, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4589-4944","authenticated-orcid":false,"given":"Haitham","family":"M. 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