{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T03:42:14Z","timestamp":1768794134190,"version":"3.49.0"},"reference-count":18,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,17]],"date-time":"2021-12-17T00:00:00Z","timestamp":1639699200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012655","name":"Universidad de Antofagasta","doi-asserted-by":"publisher","award":["Proyecto Semillero de Investigaci\u00f3n \"Modelos Estad\u00edsticos con Aplicaciones\""],"award-info":[{"award-number":["Proyecto Semillero de Investigaci\u00f3n \"Modelos Estad\u00edsticos con Aplicaciones\""]}],"id":[{"id":"10.13039\/501100012655","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this work, we present a new generalization of the student\u2019s t distribution. The new distribution is obtained by the quotient of two independent random variables. This quotient consists of a standard Normal distribution divided by the power of a chi square distribution divided by its degrees of freedom. Thus, the new symmetric distribution has heavier tails than the student\u2019s t distribution and extensions of the slash distribution. We develop a procedure to use quantile regression where the response variable or the residuals have high kurtosis. We give the density function expressed by an integral, we obtain some important properties and some useful procedures for making inference, such as moment and maximum likelihood estimators. By way of illustration, we carry out two applications using real data, in the first we provide maximum likelihood estimates for the parameters of the generalized student\u2019s t distribution, student\u2019s t, the extended slash distribution, the modified slash distribution, the slash distribution generalized student\u2019s t test, and the double slash distribution, in the second we perform quantile regression to fit a model where the response variable presents a high kurtosis.<\/jats:p>","DOI":"10.3390\/sym13122444","type":"journal-article","created":{"date-parts":[[2021,12,20]],"date-time":"2021-12-20T02:40:32Z","timestamp":1639968032000},"page":"2444","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A New Generalization of the Student\u2019s t Distribution with an Application in Quantile Regression"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2921-3056","authenticated-orcid":false,"given":"Jimmy","family":"Reyes","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1270300, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mario A.","family":"Rojas","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1270300, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0534-1774","authenticated-orcid":false,"given":"Jaime","family":"Arru\u00e9","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1270300, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1111\/j.1467-9574.1972.tb00191.x","article-title":"Understanding Some Long-Tailed Symmetrical Distributions","volume":"26","author":"Rogers","year":"1972","journal-title":"Stat. Neerl."},{"key":"ref_2","unstructured":"Mosteller, F., and Tukey, J.W. (1977). Data Analysis and Regression, Addison-Wesley."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1080\/01621459.1982.10477827","article-title":"Biweight Approach to the One-Sample Problem","volume":"77","author":"Kafadar","year":"1982","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.jspi.2004.06.023","article-title":"The multivariate skew-slash distribution","volume":"136","author":"Wang","year":"2006","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_5","first-page":"717","article-title":"A New Family of Slash-Distributions with Elliptical Contours","volume":"77","author":"Quintana","year":"2008","journal-title":"Stat. Probab. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2756","DOI":"10.1016\/j.spl.2008.03.017","article-title":"An Alternative Multivariate Skew-Slash Distribution","volume":"78","author":"Arslan","year":"2008","journal-title":"Stat. Probab. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1080\/03610910701539161","article-title":"A Generalization of the Univariate Slash by a Scale-Mixture Exponential Power Distribution","volume":"36","author":"Genc","year":"2007","journal-title":"Commun. Stat. Simul. Comput."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/j.spl.2008.08.014","article-title":"An Extension of the Generalized Birnbaum-Saunders Distribution","volume":"79","author":"Bolfarine","year":"2009","journal-title":"Stat. Probab. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1080\/02331888.2012.694441","article-title":"Modified slash distribution","volume":"47","author":"Reyes","year":"2013","journal-title":"Statistics"},{"key":"ref_10","first-page":"215","article-title":"An extension of the slash-elliptical distribution","volume":"38","author":"Rojas","year":"2014","journal-title":"Stat. Oper. Res. Trans. (SORT)"},{"key":"ref_11","unstructured":"Johnson, N.L., Kotz, S., and Balakrishnan, N. (1988). Continuous Univariate Distributions, Wiley. [2nd ed.]."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1461","DOI":"10.1007\/s00181-018-1570-0","article-title":"A review of Student\u2019s t distribution and its generalizations","volume":"58","author":"Li","year":"2020","journal-title":"Empir. Econ."},{"key":"ref_13","first-page":"3547","article-title":"The Univarite and Multivariate Generalized Slash Student Distribution","volume":"3","year":"2015","journal-title":"Int. J. Math. Its Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"459","DOI":"10.18576\/jsap\/090303","article-title":"Univariate and Multivariate Double Slash Distribution","volume":"9","author":"Tahir","year":"2020","journal-title":"J. Stat. Appl. Probab."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2025","DOI":"10.1080\/03610926.2019.1568484","article-title":"Generalized modified slash distribution with applications","volume":"49","author":"Reyes","year":"2020","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1007\/BF00297947","article-title":"Die Optische Richtungsorientierung der RotenWaldameise (Formica rufa L.)","volume":"40","author":"Jander","year":"1957","journal-title":"Z. Vgl. Physiol."},{"key":"ref_17","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_18","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\/13\/12\/2444\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:51:07Z","timestamp":1760169067000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/12\/2444"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,17]]},"references-count":18,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["sym13122444"],"URL":"https:\/\/doi.org\/10.3390\/sym13122444","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,17]]}}}