{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:59:55Z","timestamp":1760057995279,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,7]],"date-time":"2025-03-07T00:00:00Z","timestamp":1741305600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University","award":["PNURSP2025R745"],"award-info":[{"award-number":["PNURSP2025R745"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, two different families are mixed: the exponentiated and new Topp\u2013Leone-G families. This yields a new family, which we named the mixture of the exponentiated and new Topp\u2013Leone-G family. Some statistical properties of the proposed family are obtained. Then, the mixture of two exponentiated new Topp\u2013Leone inverse Weibull distribution is introduced as a sub-model from the mixture of exponentiated and new Topp\u2013Leone-G family. Some related properties are studied, such as the quantile function, moments, moment generating function, and order statistics. Furthermore, the maximum likelihood and Bayes approaches are employed to estimate the unknown parameters, reliability and hazard rate functions of the mixture of exponentiated and new Topp\u2013Leone inverse Weibull distribution. Bayes estimators are derived under both the symmetric squared error loss function and the asymmetric linear exponential loss function. The performance of maximum likelihood and Bayes estimators is evaluated through a Monte Carlo simulation. The applicability and flexibility of the MENTL-IW distribution are demonstrated by well-fitting two real-world engineering datasets. The results demonstrate the superior performance of the MENTL-IW distribution compared to other competing models.<\/jats:p>","DOI":"10.3390\/sym17030399","type":"journal-article","created":{"date-parts":[[2025,3,7]],"date-time":"2025-03-07T04:29:59Z","timestamp":1741321799000},"page":"399","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Development and Engineering Applications of a Novel Mixture Distribution: Exponentiated and New Topp\u2013Leone-G Families"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7017-8336","authenticated-orcid":false,"given":"Hebatalla H.","family":"Mohammad","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"given":"Sulafah M. S.","family":"Binhimd","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3247-2013","authenticated-orcid":false,"given":"Abeer A.","family":"EL-Helbawy","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls\u2019 Branch), Cairo 11751, Egypt"},{"name":"Higher Institute of Marketing, Commerce & Information Systems (MCI), Cairo 11511, Egypt"}]},{"given":"Gannat R.","family":"AL-Dayian","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls\u2019 Branch), Cairo 11751, Egypt"}]},{"given":"Fatma G.","family":"Abd EL-Maksoud","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Commerce, Al-Azhar University (Girls\u2019 Branch), Tafahna Al-Ashraf 44511, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0646-9443","authenticated-orcid":false,"given":"Mervat K.","family":"Abd Elaal","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls\u2019 Branch), Cairo 11751, Egypt"},{"name":"Canal High Institute of Engineering and Technology, Suez 43511, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1080\/00949659708811835","article-title":"Approximate Bayes estimation for mixture of two Weibull distributions under Type-2 censoring","volume":"58","author":"Ahmed","year":"1997","journal-title":"J. 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De Estad."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/399\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:48:43Z","timestamp":1760028523000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/399"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,7]]},"references-count":14,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["sym17030399"],"URL":"https:\/\/doi.org\/10.3390\/sym17030399","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,3,7]]}}}