{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T07:14:38Z","timestamp":1779261278427,"version":"3.51.4"},"reference-count":31,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,5,15]],"date-time":"2024-05-15T00:00:00Z","timestamp":1715731200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Education in Saudi Arabia","award":["RI-44-0439"],"award-info":[{"award-number":["RI-44-0439"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Symmetrical as well as asymmetrical statistical models play a prominent role in describing and predicting the real-world phenomena of nature. Among other fields, these models are very useful for modeling data in the sector of civil engineering. Due to the applicability of the statistical models in civil engineering and other related sectors, this paper offers a statistical methodology to improve the distributional flexibility of traditional models. The suggested method\/approach is called the extended-X family of distributions. The proposed method has the ability to generate symmetrical and asymmetrical probability distributions. Based on the extended-X family approach, an updated version of the Weibull model, namely, the extended Weibull model, is studied. The proposed model is very flexible and has the ability to capture the symmetrical and asymmetrical shapes of its density function. For the extended-X method, the estimation of parameters, a simulation study, and some mathematical properties are derived. Finally, the practical illustration\/usefulness of the suggested model is shown by analyzing two data sets taken from the field of engineering. Both data sets represent the fracture toughness of alumina (Al2O3).<\/jats:p>","DOI":"10.3390\/sym16050611","type":"journal-article","created":{"date-parts":[[2024,5,15]],"date-time":"2024-05-15T06:14:42Z","timestamp":1715753682000},"page":"611","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["A New Modification of the Weibull Distribution: Model, Theory, and Analyzing Engineering Data Sets"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5154-7477","authenticated-orcid":false,"given":"Huda M.","family":"Alshanbari","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\/0000-0003-3782-4081","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\/0000-0002-2853-0762","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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8518-9831","authenticated-orcid":false,"given":"Omalsad Hamood","family":"Odhah","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"}]},{"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":[[2024,5,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1575","DOI":"10.3934\/nhm.2023069","article-title":"A new distributional approach: Estimation, Monte Carlo simulation and applications to the biomedical data sets","volume":"18","author":"Kamal","year":"2023","journal-title":"Netw. Heterog. 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