{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:06:48Z","timestamp":1760238408029,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,8,10]],"date-time":"2020-08-10T00:00:00Z","timestamp":1597017600000},"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 paper, we propose a new three-parameter lifetime distribution for modeling symmetric real-life data sets. A simple-type Copula-based construction is presented to derive many bivariate- and multivariate-type distributions. The failure rate function of the new model can be \u201cmonotonically asymmetric increasing\u201d, \u201cincreasing-constant\u201d, \u201cmonotonically asymmetric decreasing\u201d and \u201cupside-down-constant\u201d shaped. We investigate some of mathematical symmetric\/asymmetric properties such as the ordinary moments, moment generating function, conditional moment, residual life and reversed residual functions. Bonferroni and Lorenz curves and mean deviations are discussed. The maximum likelihood method is used to estimate the model parameters. Finally, we illustrate the importance of the new model by the study of real data applications to show the flexibility and potentiality of the new model. The kernel density estimation and box plots are used for exploring the symmetry of the used data.<\/jats:p>","DOI":"10.3390\/sym12081338","type":"journal-article","created":{"date-parts":[[2020,8,10]],"date-time":"2020-08-10T09:04:16Z","timestamp":1597050256000},"page":"1338","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Generalization of Binomial Exponential-2 Distribution: Copula, Properties and Applications"],"prefix":"10.3390","volume":"12","author":[{"given":"Naif","family":"Alotaibi","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics-College of Science, Imam Mohammad ibn Saud, Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1291-9167","authenticated-orcid":false,"given":"Igor V.","family":"Malyk","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Informatics, Yuriy Fedkovych Chernivtsi National University, 28 Universytetska Street, 58012 Chernivtsi, Ukraine"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,10]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Shaked, M., and Shanthikumar, J. 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