{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T22:17:57Z","timestamp":1768342677033,"version":"3.49.0"},"reference-count":28,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,2]],"date-time":"2023-08-02T00:00:00Z","timestamp":1690934400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research, Princess Nourah bint Abdulrahman University, through the Program of Research Project Funding After Publication","award":["44-PRFA-P-88"],"award-info":[{"award-number":["44-PRFA-P-88"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Proposing new families of probability models for data modeling in applied sectors is a prominent research topic. This paper also proposes a new method based on the trigonometric function to derive the updated form of the existing probability models. The proposed family is called the cotangent trigonometric-G family of distributions. Based on the cotangent trigonometric-G method, a new version of the Weibull model, namely, the cotangent trigonometric Weibull distribution, is studied. Certain mathematical properties of the cotangent trigonometric-G family are derived. The estimators of the cotangent trigonometric-G distributions are obtained via the maximum likelihood method. The Monte Carlo simulation study is conducted to assess the performances of the estimators. Finally, two applications from the health sector are considered to illustrate the cotangent trigonometric-G method. Based on seven evaluating criteria, it is observed that the cotangent trigonometric-G significantly improves the fitting power of the existing models.<\/jats:p>","DOI":"10.3390\/sym15081528","type":"journal-article","created":{"date-parts":[[2023,8,2]],"date-time":"2023-08-02T11:04:38Z","timestamp":1690974278000},"page":"1528","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["A Novel Probabilistic Approach Based on Trigonometric Function: Model, Theory with Practical Applications"],"prefix":"10.3390","volume":"15","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"}]},{"given":"Faridoon","family":"Khan","sequence":"additional","affiliation":[{"name":"Pakistan Institute of Development Economics, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2853-0762","authenticated-orcid":false,"given":"Abd Al-Aziz Hosni","family":"El-Bagoury","sequence":"additional","affiliation":[{"name":"Basic Sciences Department, Higher Institute of Engineering and Technology, EL-Mahala EL-Kobra 31511, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"19477","DOI":"10.3934\/math.2023994","article-title":"Univariate and multivariate analyses of the asset returns using new statistical models and penalized regression techniques","volume":"8","author":"Alshanbari","year":"2023","journal-title":"Aims Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"9819200","DOI":"10.1155\/2021\/9819200","article-title":"A flexible extension of pareto distribution: Properties and applications","volume":"2021","author":"Alshanbari","year":"2021","journal-title":"Comput. 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