{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,16]],"date-time":"2024-07-16T10:37:11Z","timestamp":1721126231500},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,3]],"date-time":"2023-02-03T00:00:00Z","timestamp":1675382400000},"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":"The primary objective of this article was to introduce a new probabilistic model for the discussion and analysis of random covariates. The introduced model was derived based on the Marshall\u2013Olkin shock model. After proposing the mathematical form of the new bivariate model, some of its distributional properties, including joint probability distribution, joint reliability distribution, joint reversed (hazard) rate distribution, marginal probability density function, conditional probability density function, moments, and distributions for both Y=max{X1,X2} and W=min{X1,X2}, were investigated. This novel model can be applied to discuss and evaluate symmetric and asymmetric data under various kinds of dispersion. Moreover, it can be used as a probability approach to analyze different shapes of hazard rates. The maximum likelihood approach was utilized for estimating the parameters of the bivariate model. A simulation study was carried out to assess the performance of the parameters, and it was noted that the maximum likelihood technique can be used to generate consistent estimators. Finally, two real datasets were analyzed to illustrate the notability of the novel bivariate distribution, and it was found that the suggested distribution provided a better fit than the competitive bivariate models.<\/jats:p>","DOI":"10.3390\/sym15020411","type":"journal-article","created":{"date-parts":[[2023,2,3]],"date-time":"2023-02-03T10:31:24Z","timestamp":1675420284000},"page":"411","source":"Crossref","is-referenced-by-count":2,"title":["A Bivariate Extension to Exponentiated Inverse Flexible Weibull Distribution: Shock Model, Features, and Inference to Model Asymmetric Data"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-7585-5519","authenticated-orcid":false,"given":"Mahmoud","family":"El-Morshedy","sequence":"first","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"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-5619-210X","authenticated-orcid":false,"given":"Mohamed S.","family":"Eliwa","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia"},{"name":"Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy"},{"name":"Department of Statistics and Computer Science, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-2157-3997","authenticated-orcid":false,"given":"Muhammad H.","family":"Tahir","sequence":"additional","affiliation":[{"name":"Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-6638-2185","authenticated-orcid":false,"given":"Morad","family":"Alizadeh","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr 75168, Iran"}]},{"given":"Rana","family":"El-Desokey","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]},{"given":"Afrah","family":"Al-Bossly","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"}]},{"given":"Hana","family":"Alqifari","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1080\/01621459.1967.10482885","article-title":"A multivariate exponential distribution","volume":"62","author":"Marshall","year":"1967","journal-title":"J. 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Edge"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/2\/411\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,3]],"date-time":"2023-02-03T11:00:46Z","timestamp":1675422046000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/2\/411"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,3]]},"references-count":24,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["sym15020411"],"URL":"https:\/\/doi.org\/10.3390\/sym15020411","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,3]]}}}