{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T16:51:16Z","timestamp":1766076676733,"version":"3.48.0"},"reference-count":23,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T00:00:00Z","timestamp":1766016000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004242","name":"Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia","doi-asserted-by":"publisher","award":["PNURSP2025R744"],"award-info":[{"award-number":["PNURSP2025R744"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper introduces the bivariate bounded Gompertz\u2013log-logistic (BBGLL) distribution, a bounded bivariate lifetime model built by coupling two bounded Gompertz\u2013log-logistic marginals through a Clayton copula with an independent dependence parameter. The proposed model effectively describes positively dependent lifetimes within finite support and accommodates increasing, decreasing, and bathtub-shaped hazard rates. Analytical expressions for the survival functions, hazard rate functions, and joint moments are derived, while measures of association such as Kendall\u2019s tau, Spearman\u2019s rho, and tail-dependence coefficients characterize the dependence structure. Parameters are estimated via maximum likelihood, inference functions for margins (IFM), and semi-parametric methods, with performance assessed through Monte Carlo simulations. A real-life data application illustrates the practical relevance of the model, showing that the BBGLL distribution achieves a superior goodness-of-fit relative to existing bivariate alternatives, highlighting its practical usefulness.<\/jats:p>","DOI":"10.3390\/axioms14120930","type":"journal-article","created":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T16:42:05Z","timestamp":1766076125000},"page":"930","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Flexible Bivariate Lifetime Model with Upper Bound: Theoretical Development and Lifetime Application"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-1149-8244","authenticated-orcid":false,"given":"Shuhrah","family":"Alghamdi","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Princess Nourah bint Abdulrahman University, Riyadh 11564, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9942-6268","authenticated-orcid":false,"given":"Tassaddaq","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur 10250, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6075-4328","authenticated-orcid":false,"given":"Maher","family":"Kachour","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Natural Sciences, Gulf University for Science and Technology, P.O. Box 7207, Hawally 32093, Kuwait"},{"name":"Center of Applied Mathematics and Bioinformatics (CAMB), Gulf University for Science and Technology, P.O. Box 7207, Hawally 32093, Kuwait"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1016\/j.ress.2005.05.008","article-title":"The beta exponential distribution","volume":"91","author":"Nadarajah","year":"2006","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1399","DOI":"10.1016\/j.jfranklin.2010.06.010","article-title":"The Kumaraswamy Weibull distribution with application to failure data","volume":"347","author":"Cordeiro","year":"2010","journal-title":"J. Frankl. 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