{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T09:29:20Z","timestamp":1770283760177,"version":"3.49.0"},"reference-count":25,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T00:00:00Z","timestamp":1607558400000},"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 paper, we reparameterized the extended exponential model based on the mean in order to include covariates and facilitate the interpretation of the coefficients. The model is compared with common models defined in the positive line also reparametrized in the mean. Parameter estimation is approached based on the expectation\u2013maximization algorithm. Furthermore, we discuss residuals and influence diagnostic tools. A simulation study for recovered parameters is presented. Finally, an application illustrating the advantages of the model in a real data set is presented.<\/jats:p>","DOI":"10.3390\/sym12122042","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T22:15:36Z","timestamp":1607638536000},"page":"2042","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Extended Exponential Regression Model: Diagnostics and Application to Mineral Data"],"prefix":"10.3390","volume":"12","author":[{"given":"Yolanda M.","family":"G\u00f3mez","sequence":"first","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\/0000-0001-8184-7403","authenticated-orcid":false,"given":"Diego I.","family":"Gallardo","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ingenier\u00eda, Universidad de Atacama, Copiap\u00f3 1530000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jeremias","family":"Le\u00e3o","sequence":"additional","affiliation":[{"name":"Departamento de Estat\u00edstica, Universidade Federal do Amazonas, Manaus-AM 69001-000, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3726-5507","authenticated-orcid":false,"given":"H\u00e9ctor W.","family":"G\u00f3mez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1017\/S0305004100015681","article-title":"Limiting forms of the frequency distribution of the largest and smallest member of a sample","volume":"24","author":"Fisher","year":"1928","journal-title":"Proc. Camb. Philos. Soc."},{"key":"ref_2","first-page":"25","article-title":"A New Extension of the Exponential Distribution","volume":"37","author":"Bolfarine","year":"2014","journal-title":"Colomb. J. Stat."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1016\/j.matcom.2007.06.007","article-title":"Lindley distribution and its application","volume":"78","author":"Ghitany","year":"2008","journal-title":"Math. Comput. Simul."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"393","DOI":"10.6339\/JDS.201607_14(3).0001","article-title":"The exponentiated generalized extended exponential distribution","volume":"14","author":"Andrade","year":"2016","journal-title":"J. Data Sci."},{"key":"ref_5","first-page":"383","article-title":"The Modified Exponential Distribution with Applications","volume":"33","author":"Rasekhi","year":"2017","journal-title":"Pak. J. Stat."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3043","DOI":"10.2298\/FIL1808043R","article-title":"Discrete Weighted Exponential Distribution: Properties and Applications","volume":"32","author":"Rasekhi","year":"2018","journal-title":"Filomat"},{"key":"ref_7","first-page":"2825","article-title":"Reparameterized Birnbaum\u2013Saunders regression models with varying precision","volume":"10","author":"Cysneiros","year":"2016","journal-title":"Electron. J. Stat."},{"key":"ref_8","unstructured":"Bourguignon, M., Santos-Neto, M., and de Castro, M. (2018). A new regression model for positive data. arXiv."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2002","DOI":"10.1002\/bimj.201900132","article-title":"Parametric modal regression with varying precision","volume":"62","author":"Bourguignon","year":"2020","journal-title":"Biom. J."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","article-title":"Maximum likelihood from incomplete data via the EM algorithm (with discussion)","volume":"39","author":"Dempster","year":"1977","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1080\/00401706.1977.10489493","article-title":"Detection of influential observation in linear regression","volume":"19","author":"Cook","year":"1977","journal-title":"Technometrics"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1111\/j.2517-6161.1986.tb01398.x","article-title":"Assessment of local influence","volume":"48","author":"Cook","year":"1986","journal-title":"J. R. Stat. Soc. Ser. 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Symmetry, 11.","DOI":"10.3390\/sym11060835"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/S0167-9473(02)00303-1","article-title":"Influence analyses of nonlinear mixed-effects models","volume":"45","author":"Lee","year":"2004","journal-title":"Comput. Statist. Data Anal."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1080\/10618600.1996.10474708","article-title":"Randomized quantile residuals","volume":"5","author":"Dunn","year":"1996","journal-title":"J. Comput. Graph. Stat."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1111\/j.2517-6161.1968.tb00724.x","article-title":"A general definition of residuals","volume":"30","author":"Cox","year":"1968","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"ref_19","unstructured":"R Development Core Team (2019). A Language and Environment for Statistical Computing, R Foundation for Statistical Computing."},{"key":"ref_20","first-page":"395","article-title":"Skew-symmetric distributions generated by the distribution function of the normal distribution","volume":"18","author":"Venegas","year":"2006","journal-title":"Envirometrics"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1002\/cem.1378","article-title":"The log-bimodal-skew-normal model. A geochemical application","volume":"25","author":"Bolfarine","year":"2011","journal-title":"J. Chemom."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"875","DOI":"10.1007\/s00362-011-0391-4","article-title":"An extension of the half-normal distribution","volume":"53","author":"Olmos","year":"2012","journal-title":"Stat. Pap."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Reyes, J., Barranco-Chamorro, I., Gallardo, D.I., and G\u00f3mez, H.W. (2018). Generalized Modified Slash Birnbaum\u2013Saunders Distribution. Symmetry, 10.","DOI":"10.3390\/sym10120724"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","article-title":"A new look at the statistical model identification","volume":"19","author":"Akaike","year":"1974","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1214\/aos\/1176344136","article-title":"Estimating the dimension of a model","volume":"6","author":"Schwarz","year":"1978","journal-title":"Ann. Stat."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/12\/2042\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:43:07Z","timestamp":1760179387000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/12\/2042"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,10]]},"references-count":25,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["sym12122042"],"URL":"https:\/\/doi.org\/10.3390\/sym12122042","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,10]]}}}