{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T04:30:05Z","timestamp":1768710605181,"version":"3.49.0"},"reference-count":33,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,6,23]],"date-time":"2023-06-23T00:00:00Z","timestamp":1687478400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Estudio de la Deserci\u00f3n en los Programas de Pregrado de la Universidad de C\u00f3rdoba Usando Diferentes Metodolog\u00edas estad\u00edsticas","award":["FCB-06-22"],"award-info":[{"award-number":["FCB-06-22"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we propose a nonlinear regression model with exponentiated skew-elliptical errors distributed, which can be fitted to datasets with high levels of asymmetry and kurtosis. Maximum likelihood estimation procedures in finite samples are discussed and the information matrix is deduced. We carried out a diagnosis of the influence for the nonlinear model. To analyze the sensitivity of the maximum likelihood estimators of the model\u2019s parameters to small perturbations in distribution assumptions and parameter estimation, we studied the perturbation schemes, the case weight, and the explanatory and response variables of perturbations; we also carried out a residual analysis of the deviance components. Simulation studies were performed to assess some properties of the estimators, showing the good performance of the proposed estimation procedure in finite samples. Finally, an application to a real dataset is presented.<\/jats:p>","DOI":"10.3390\/axioms12070624","type":"journal-article","created":{"date-parts":[[2023,6,26]],"date-time":"2023-06-26T05:28:02Z","timestamp":1687757282000},"page":"624","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An Exponentiated Skew-Elliptic Nonlinear Extension to the Log\u2013Linear Birnbaum\u2013Saunders Model with Diagnostic and Residual Analysis"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6441-5377","authenticated-orcid":false,"given":"Guillermo","family":"Mart\u00ednez-Fl\u00f3rez","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica y Estad\u00edstica, Facultad de Ciencias B\u00e1sicas, Universidad de C\u00f3rdoba, Monter\u00eda 230002, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8092-9666","authenticated-orcid":false,"given":"Yolanda M.","family":"G\u00f3mez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ingenier\u00eda, Universidad de Atacama, Copiap\u00f3 1530000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6643-6972","authenticated-orcid":false,"given":"Osvaldo","family":"Venegas","sequence":"additional","affiliation":[{"name":"Departamento de Ciencias Matem\u00e1ticas y F\u00edsicas, Facultad de Ingenier\u00eda, Universidad Cat\u00f3lica de Temuco, Temuco 4780000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1007\/s00362-008-0139-y","article-title":"A nonlinear regression model with skew-normal errors","volume":"51","author":"Cancho","year":"2010","journal-title":"Stat. 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