{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T07:16:30Z","timestamp":1779261390231,"version":"3.51.4"},"reference-count":23,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T00:00:00Z","timestamp":1693353600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Princess Nourah bint Abdulrahman University","award":["FRP-1444-10"],"award-info":[{"award-number":["FRP-1444-10"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Modeling and predicting time-to-event phenomena in engineering, sports, and medical sectors are very crucial. Numerous models have been proposed for modeling such types of data sets. These models are introduced by adding one or more parameters to the traditional distributions. The addition of new parameters to the traditional distributions leads to serious issues, such as estimation consequences and re-parametrization problems. To avoid such problems, this paper introduces a new method for generating new probability distributions without any additional parameters. The proposed method may be called a weighted cosine-G family of distributions. Different distributional properties of the weighted cosine-G family, along with the maximum likelihood estimators, are obtained. A special model of the weighted cosine-G family, by utilizing the Weibull model, is considered. The special model of the weighted cosine-G family may be called a weighted cosine-Weibull distribution. A simulation study of the weighted cosine-Weibull model is conducted to evaluate the performances of its estimators. Finally, the applications of the weighted cosine-Weibull distribution are shown by considering three data sets related to the time-to-event phenomena.<\/jats:p>","DOI":"10.3390\/axioms12090849","type":"journal-article","created":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T10:30:52Z","timestamp":1693391452000},"page":"849","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["A Weighted Cosine-G Family of Distributions: Properties and Illustration Using Time-to-Event Data"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8518-9831","authenticated-orcid":false,"given":"Omalsad Hamood","family":"Odhah","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5154-7477","authenticated-orcid":false,"given":"Huda M.","family":"Alshanbari","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3782-4081","authenticated-orcid":false,"given":"Zubair","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Statistics, Quaid-i-Azam University, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3683-5486","authenticated-orcid":false,"given":"Gadde Srinivasa","family":"Rao","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Dodoma, Dodoma P.O. Box 259, Tanzania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Almarashi, A.M., Algarni, A., and Nassar, M. (2020). On estimation procedures of stress-strength reliability for Weibull distribution with application. PLoS ONE, 15.","DOI":"10.1371\/journal.pone.0237997"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Zhao, W., Khosa, S.K., Ahmad, Z., Aslam, M., and Afify, A.Z. (2020). Type-I heavy tailed family with applications in medicine, engineering and insurance. PLoS ONE, 15.","DOI":"10.1371\/journal.pone.0237462"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"101582","DOI":"10.1016\/j.jksus.2021.101582","article-title":"Modeling engineering data using extended power-Lindley distribution: Properties and estimation methods","volume":"33","author":"Kumar","year":"2021","journal-title":"J. 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