{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T03:22:54Z","timestamp":1775704974899,"version":"3.50.1"},"reference-count":38,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2022,1,30]],"date-time":"2022-01-30T00:00:00Z","timestamp":1643500800000},"content-version":"vor","delay-in-days":29,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2022,1]]},"abstract":"<jats:p>\n                    Due to the advance computer technology, the use of probability distributions has been raised up to solve the real life problems. These applications are found in reliability engineering, computer sciences, economics, psychology, survival analysis, and some others. This study offers a new probability model called Marshall\u2013Olkin Extended Gumbel Type\u2010II (MOEGT\u2010II) which can model various shapes of the failure rate function. The proposed distribution is capable to model increasing, decreasing, reverse J\u2010shaped, and upside down bathtub shapes of the failure rate function. Various statistical properties of the proposed distribution are derived such as alternate expressions for the density and distribution function, special cases of MOEGT\u2010II distribution, quantile function, Lorenz curve, and Bonferroni curve. Estimation of the unknown parameters is carried out by the method of maximum likelihood. A simulation study is conducted using three different iterative methods with different samples of sizes\n                    <jats:italic>n<\/jats:italic>\n                    . The usefulness and potentiality of the MOEGT\u2010II distribution have been shown using three real life data sets. The MOEGT\u2010II distribution has been demonstrated as better fit than Exponentiated Gumbel Type\u2010II (EGT\u2010II), Marshall\u2013Olkin Gumbel Type\u2010II (MOGT\u2010II), Gumbel Type\u2010II (GT\u2010II), Marshall\u2013Olkin\u2013Frechet (MOF), Frechet (F), Burr III, Log Logistic (LL), Beta Inverse Weibull (BIW), and Kumaraswamy Inverse Weibull (KIW) distributions.\n                  <\/jats:p>","DOI":"10.1155\/2022\/2219570","type":"journal-article","created":{"date-parts":[[2022,1,30]],"date-time":"2022-01-30T21:07:15Z","timestamp":1643576835000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Marshall\u2013Olkin Extended Gumbel Type\u2010II Distribution: Properties and Applications"],"prefix":"10.1155","volume":"2022","author":[{"given":"Farwa","family":"Willayat","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Naz","family":"Saud","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1403-7093","authenticated-orcid":false,"given":"Muhammad","family":"Ijaz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anita","family":"Silvianita","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7585-5519","authenticated-orcid":false,"given":"Mahmoud","family":"El-Morshedy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2022,1,30]]},"reference":[{"key":"e_1_2_14_1_2","first-page":"419","article-title":"Use of gamma distribution in hydrological analysis","volume":"24","author":"Aksoy H.","year":"2000","journal-title":"Turkish Journal of Engineering and Environmental Sciences"},{"key":"e_1_2_14_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/bf00552092"},{"key":"e_1_2_14_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0960-1481(01)00151-3"},{"key":"e_1_2_14_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0265-931x(02)00025-5"},{"key":"e_1_2_14_5_2","doi-asserted-by":"publisher","DOI":"10.1111\/1467-842x.00072"},{"key":"e_1_2_14_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/1521-4036(200102)43:1<117::aid-bimj117>3.0.co;2-r"},{"key":"e_1_2_14_7_2","doi-asserted-by":"publisher","DOI":"10.6339\/JDS.201301_11(1).0001"},{"key":"e_1_2_14_8_2","doi-asserted-by":"publisher","DOI":"10.15446\/rce.v38n1.48806"},{"key":"e_1_2_14_9_2","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/84.3.641"},{"key":"e_1_2_14_10_2","first-page":"117","article-title":"Marshall-olkin pareto processes","volume":"9","author":"Alice T.","year":"2003","journal-title":"Far East Journal of Theoretical Statistics"},{"key":"e_1_2_14_11_2","doi-asserted-by":"publisher","DOI":"10.1080\/02664760500165008"},{"key":"e_1_2_14_12_2","doi-asserted-by":"publisher","DOI":"10.1080\/03610920601126571"},{"key":"e_1_2_14_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00362-008-0173-9"},{"key":"e_1_2_14_14_2","unstructured":"JoseK. 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