{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T17:38:08Z","timestamp":1778953088673,"version":"3.51.4"},"reference-count":21,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,7,8]],"date-time":"2020-07-08T00:00:00Z","timestamp":1594166400000},"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>Data from some research fields tend to exhibit a positive skew. For example, in experimental psychology, reaction times (RTs) are characterised as being positively skewed. However, it is not unlikely that RTs can take a normal or, even, a negative shape. While the Ex-Gaussian distribution is suitable to model positively skewed data, it cannot cope with negatively skewed data. This manuscript proposes a distribution that can deal with both negative and positive skews: the exponential-centred skew-normal (ECSN) distribution. The mathematical properties of the proposed distribution are reported, and it is featured in two non-synthetic datasets.<\/jats:p>","DOI":"10.3390\/sym12071140","type":"journal-article","created":{"date-parts":[[2020,7,10]],"date-time":"2020-07-10T09:45:31Z","timestamp":1594374331000},"page":"1140","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["The Exponential-Centred Skew-Normal Distribution"],"prefix":"10.3390","volume":"12","author":[{"given":"Guillermo","family":"Mart\u00ednez-Fl\u00f3rez","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas y Estad\u00edstica, Facultad de Ciencias B\u00e1sicas, Universidad de C\u00f3rdoba, C\u00f3rdoba 2300, Colombia"},{"name":"Programa de P\u00f3s-Gradua\u00e7\u00e3o em Modelagem e M\u00e9todos Quantitativos, Universidade Federal do Cear\u00e1, Fortaleza 60020-181, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7288-7710","authenticated-orcid":false,"given":"Carlos","family":"Barrera-Causil","sequence":"additional","affiliation":[{"name":"Davinci Research Group, Faculty of Applied and Exact Sciences, Metropolitan Technological Institute, Medell\u00edn 050034, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4680-1287","authenticated-orcid":false,"given":"Fernando","family":"Marmolejo-Ramos","sequence":"additional","affiliation":[{"name":"Centre for Change and Complexity in Learning, The University of South Australia, Adelaide 5000, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1037\/h0021740","article-title":"Inferred components of reaction times as functions of foreperiod duration","volume":"69","author":"Hohle","year":"1965","journal-title":"J. Exp. Psychol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/s11571-017-9473-x","article-title":"Fatigue-life distributions for reaction time data","volume":"12","author":"Tejo","year":"2018","journal-title":"Cogn. Neurodyn."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/s11571-019-09532-1","article-title":"Theoretical models of reaction times arising from simple-choice tasks","volume":"13","author":"Tejo","year":"2019","journal-title":"Cogn. Neurodyn."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1007\/s00422-015-0651-9","article-title":"Modeling neural activity with cumulative damage distributions","volume":"109","author":"Leiva","year":"2015","journal-title":"Biol. Cybern."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Mart\u00ednez-Fl\u00f3rez, G., Barranco-Chamorro, I., Bolfarine, H., and G\u00f3mez, H. (2019). Flexible Birnbaum\u2013Saunders distribution. Symmetry, 11.","DOI":"10.3390\/sym11101305"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Iriarte, Y., Varela, H., G\u00f3mez, H., and G\u00f3mez, H. (2020). A Gamma-Type distribution with applications. Symmetry, 12.","DOI":"10.3390\/sym12050870"},{"key":"ref_7","first-page":"309","article-title":"Stochastic latency mechanisms","volume":"Volume 1","author":"Luce","year":"1963","journal-title":"Handbook of Mathematical Psychology"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/BF02477834","article-title":"Decision structure and time relations in simple choice behavior","volume":"18","author":"Christie","year":"1956","journal-title":"Bull. Math. Biophys."},{"key":"ref_9","first-page":"171","article-title":"A class of distributions which includes the normal ones","volume":"12","author":"Azzalini","year":"1985","journal-title":"Scand. J. Stat."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Azzalini, A., and Capitanio, A. (2013). The Skew-Normal and Related Families, Cambridge University Press. [1st ed.].","DOI":"10.1017\/CBO9781139248891"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1111\/j.1467-9469.2004.03_007.x","article-title":"Flexible class of skew-symmetric distributions","volume":"31","author":"Ma","year":"2004","journal-title":"Scand. J. Stat."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1733","DOI":"10.1021\/ac60319a011","article-title":"Characterization of exponentially modified Gaussian peaks in chromatography","volume":"44","author":"Grushka","year":"1972","journal-title":"Anal. Chem."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1649","DOI":"10.1029\/92WR00554","article-title":"Distributions of fractional order statistics in hydrology","volume":"28","author":"Durrans","year":"1992","journal-title":"Water Resour. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1007\/s11749-011-0280-0","article-title":"Likelihood-based inference for power distributions","volume":"21","author":"Pewsey","year":"2012","journal-title":"Test"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1414","DOI":"10.1080\/02331888.2013.826659","article-title":"Skew-normal alpha-power model","volume":"48","author":"Bolfarine","year":"2014","journal-title":"Statistics"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"243","DOI":"10.2307\/3318576","article-title":"Likelihood-based inference with singular information matrix","volume":"6","author":"Rotnitzky","year":"2000","journal-title":"Bernoulli"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1111\/1467-9868.00194","article-title":"Statistical Applications of the Multivariate Skew Normal Distribution","volume":"61","author":"Azzalini","year":"1999","journal-title":"J. R. Stat. Soc."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.cognition.2010.05.010","article-title":"Testing the theory of embodied cognition with subliminal words","volume":"116","author":"Ansorge","year":"2010","journal-title":"Cognition"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Schotanus-Dijkstra, M., ten Klooster, P., Drossaert, C., Pieterse, M., Bolier, L., Walburg, J., and Bohlmeijer, E. (2016). Validation of the Flourishing Scale in a sample of people with suboptimal levels of mental well-being. BMC Psychol., 4.","DOI":"10.1186\/s40359-016-0116-5"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","article-title":"A new look at statistical model identification","volume":"19","author":"Akaike","year":"1974","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_21","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\/7\/1140\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:48:53Z","timestamp":1760176133000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/7\/1140"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,8]]},"references-count":21,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2020,7]]}},"alternative-id":["sym12071140"],"URL":"https:\/\/doi.org\/10.3390\/sym12071140","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7,8]]}}}