{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T03:19:43Z","timestamp":1770520783185,"version":"3.49.0"},"reference-count":20,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,18]],"date-time":"2021-09-18T00:00:00Z","timestamp":1631923200000},"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>In this article, a new flexible probability density function with three parameters is proposed for modeling asymmetric data (positive and negative) with different types of kurtosis (mesokurtic, leptokurtic and platykurtic). Some of its statistical and reliability properties, including hazard rate function, moments, moment generating function, incomplete moments, mean deviations, moment of the residual life, moment of the reversed residual life, and order statistics are derived. Its hazard rate function can be either constant, increasing-constant, decreasing-constant, U shape, upside down shape or upside down-U shape. Seven classical estimation methods are considered to estimate the unknown model parameters. Monte Carlo simulation experiments are performed to compare the performance of the seven different estimation methods. Finally, a distinctive asymmetric real data application is analyzed for illustrating the flexibility of the new model.<\/jats:p>","DOI":"10.3390\/sym13091730","type":"journal-article","created":{"date-parts":[[2021,9,21]],"date-time":"2021-09-21T22:35:20Z","timestamp":1632263720000},"page":"1730","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Modeling Extreme Values Utilizing an Asymmetric Probability Function"],"prefix":"10.3390","volume":"13","author":[{"given":"Mohammed M. A.","family":"Almazah","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Sciences and Arts (Muhyil), King Khalid University, Muhyil 61421, Saudi Arabia"},{"name":"Department of Mathematics and Computer, College of Sciences, Ibb University, Ibb 70270, Yemen"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9011-835X","authenticated-orcid":false,"given":"Muqrin A.","family":"Almuqrin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science in Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5619-210X","authenticated-orcid":false,"given":"Mohamed. S.","family":"Eliwa","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7585-5519","authenticated-orcid":false,"given":"Mahmoud","family":"El-Morshedy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4589-4944","authenticated-orcid":false,"given":"Haitham M.","family":"Yousof","sequence":"additional","affiliation":[{"name":"Department of Statistics, Mathematics and Insurance, Benha University, Benha 13518, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1080\/02331881003678678","article-title":"An extension of the exponential distribution","volume":"45","author":"Nadarajah","year":"2011","journal-title":"Statistics"},{"key":"ref_2","first-page":"312","article-title":"A new useful three-parameter extension of the exponential distribution","volume":"50","author":"Lemonte","year":"2016","journal-title":"Statistics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2159","DOI":"10.1080\/02664763.2015.1021669","article-title":"New flexible models generated by gamma random variables for lifetime modeling","volume":"42","author":"Ortega","year":"2015","journal-title":"J. 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