{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T22:08:22Z","timestamp":1776204502726,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,6,12]],"date-time":"2019-06-12T00:00:00Z","timestamp":1560297600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>One of the most prominent statistical distributions is the Weibull distribution. The recent modifications in this distribution have enhanced its application but only in specific fields. To introduce a more generalized Weibull distribution, in this work beta exponentiated modified Weibull distribution is established. This distribution consolidate the exponential, skewed and symmetric shapes into one density. The proposed distribution also contains nineteen lifetime distributions as a special case, which shows the flexibility of the distribution. The statistical properties of the proposed model are derived and discussed, including reliability analysis and order statistics. The hazard function of the proposed distribution can have a unimodal, decreasing, bathtub, upside-down bathtub, and increasing shape that make it effective in reliability analysis. The parameters of the proposed model are evaluated by maximum likelihood and least squares estimation methods. The significance of the beta exponentiated modified Weibull distribution for modeling is illustrated by the study of real data. The numerical study indicates that the new proposed distribution gives better results than other comparable distributions.<\/jats:p>","DOI":"10.3390\/sym11060781","type":"journal-article","created":{"date-parts":[[2019,6,12]],"date-time":"2019-06-12T10:55:19Z","timestamp":1560336919000},"page":"781","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Beta Exponentiated Modified Weibull Distribution: Properties and Application"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7310-9144","authenticated-orcid":false,"given":"Mirza Naveed","family":"Shahzad","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Gujrat, Gujrat 50700, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ehsan","family":"Ullah","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Gujrat, Gujrat 50700, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abid","family":"Hussanan","sequence":"additional","affiliation":[{"name":"Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam"},{"name":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1115\/1.4010337","article-title":"A statistical distribution function of wide applicability","volume":"103","author":"Weibull","year":"1951","journal-title":"J. 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