{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T20:37:09Z","timestamp":1777667829827,"version":"3.51.4"},"reference-count":36,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,17]],"date-time":"2024-11-17T00:00:00Z","timestamp":1731801600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Saud University, Riyadh, Saudi Arabia","award":["RSPD2024R538"],"award-info":[{"award-number":["RSPD2024R538"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this research, we present a new distribution, which is the bivariate alpha power Burr-XII distribution, based on the alpha power Burr-XII distribution. We thoroughly examine the key features of our newly developed bivariate model. We introduce a new class of bivariate models, which are built with the copula function. The statistical properties of the proposed distribution, such as conditional distributions, conditional expectations, marginal distributions, moment-generating functions, and product moments were studied. This was accomplished with two datasets of real data that came from two distinct devices. We employed Bayesian, maximum likelihood estimation, and least squares estimation strategies to obtain estimated points and intervals. Additionally, we generated bootstrap confidence intervals and conducted numerical analyses using the Markov chain Monte Carlo method. Lastly, we compared this novel bivariate distribution\u2019s performance to earlier bivariate models, to determine how well it fit the real data.<\/jats:p>","DOI":"10.3390\/axioms13110796","type":"journal-article","created":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T11:58:07Z","timestamp":1732017487000},"page":"796","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Bayesian and Non-Bayesian Inference to Bivariate Alpha Power Burr-XII Distribution with Engineering Application"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0712-9416","authenticated-orcid":false,"given":"Dina A.","family":"Ramadan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7680-6762","authenticated-orcid":false,"given":"Mustafa M.","family":"Hasaballah","sequence":"additional","affiliation":[{"name":"Department of Basic Science, Marg Higher Institute for Engineering and Modern Technology, Cairo 11721, Egypt"}]},{"given":"Nada K.","family":"Abd-Elwaha","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]},{"given":"Arwa M.","family":"Alshangiti","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}]},{"given":"Mahmoud I.","family":"Kamel","sequence":"additional","affiliation":[{"name":"Department of Basic Science, Giza Engineering Institute, Giza 12519, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8870-9692","authenticated-orcid":false,"given":"Oluwafemi Samson","family":"Balogun","sequence":"additional","affiliation":[{"name":"Department of Computing, University of Eastern Finland, FI-70211 Kuopio, Finland"}]},{"given":"Mahmoud M.","family":"El-Awady","sequence":"additional","affiliation":[{"name":"Basic Sciences Department, Misr Higher Institute for Commerce and Computers, Mansoura 35511, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,17]]},"reference":[{"key":"ref_1","unstructured":"Nelsen, R.B. (2007). An Introduction to Copulas, Springer Science Business Media."},{"key":"ref_2","unstructured":"Flores, A.Q. (2009, January 3\u20136). 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