{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T22:01:22Z","timestamp":1763071282742,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,18]],"date-time":"2023-09-18T00:00:00Z","timestamp":1694995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior-Brasil (CAPES) and Conselho Nacional de Desenvolvimento Cientifico e Tecnol\u00f3gico (CNPq)"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We use the Clayton and Frank copulas and the exponentiated odd log-logistic family to define a new flexible bivariate model to fit bimodal and asymmetry data. The copulas allow different distributions for the response variable, thus making analysis more suitable. We present some structural properties of the new model and describe a simulation study to show the consistency of the estimators. We construct a bivariate regression model based on the new family to fit oak lettuce plant data for different concentrations of silicon dioxide and organosilicon compounds. We check the response variables fresh weight and plant height together in order to verify the existing correlation between them. These variables exhibit a bimodal form, and the family used is able to model this behavior. Different marginal distributions are selected, which is an interesting point of the copula methodology. The variables have strong positive dependence, and the experiment is carried out comparing the control treatment with others leading to the following results: (i) the treatment 1-ethoxysilatrane (with concentrations 5 \u00d7 10\u22124 mL\u00b7L\u22121 and 10\u22123 mL\u00b7L\u22121) is not significant for the response variables; (ii) the treatment amorphous silicon dioxide (with concentrations 50 mg\u00b7L\u22121 and 100 mg\u00b7L\u22121) and the same treatment (with concentrations 5 \u00d7 10\u22123 mL\u00b7L\u22121 and 10\u22122 mL\u00b7L\u22121) are significant and have positive effects on both responses; (iii) the treatment amorphous silicon dioxide (with concentrations 200 mg\u00b7L\u22121 and 300 mg\u00b7L\u22121) are significant and have negative effects on the response variables. Overall, the proposed bivariate model is suitable for the current data and can be useful in other applications.<\/jats:p>","DOI":"10.3390\/sym15091778","type":"journal-article","created":{"date-parts":[[2023,9,18]],"date-time":"2023-09-18T02:17:30Z","timestamp":1695003450000},"page":"1778","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A New Bivariate Family Based on Archimedean Copulas: Simulation, Regression Model and Application"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1985-8141","authenticated-orcid":false,"given":"Gabriela M.","family":"Rodrigues","sequence":"first","affiliation":[{"name":"Department of Exact Sciences, University of S\u00e3o Paulo, Piracicaba 13418-900, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3999-7402","authenticated-orcid":false,"given":"Edwin M. M.","family":"Ortega","sequence":"additional","affiliation":[{"name":"Department of Exact Sciences, University of S\u00e3o Paulo, Piracicaba 13418-900, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1073-0114","authenticated-orcid":false,"given":"Roberto","family":"Vila","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Brasilia, Brasilia 70910-900, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3052-6551","authenticated-orcid":false,"given":"Gauss M.","family":"Cordeiro","sequence":"additional","affiliation":[{"name":"Department of Statistics, Federal University of Pernambuco, Recife 50670-901, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3277","DOI":"10.1080\/03610928608829309","article-title":"Properties of a one-parameter family of bivariate distributions with specified marginals","volume":"15","author":"Nelsen","year":"1986","journal-title":"Commun. 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