{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T12:14:17Z","timestamp":1778501657510,"version":"3.51.4"},"reference-count":13,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2019,11,1]],"date-time":"2019-11-01T00:00:00Z","timestamp":1572566400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["11160670"],"award-info":[{"award-number":["11160670"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]},{"name":"SEMILLERO","award":["UA-2019"],"award-info":[{"award-number":["UA-2019"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we obtain a matrix formula of order      n  \u2212 1 \/ 2   ,     where n is the sample size, for the skewness coefficient of the distribution of the maximum likelihood estimators in the Weibull censored data. The present result is a nice approach to verify if the assumption of the normality of the regression parameter distribution is satisfied. Also, the expression derived is simple, as one only has to define a few matrices. We conduct an extensive Monte Carlo study to illustrate the behavior of the skewness coefficient and we apply it in two real datasets.<\/jats:p>","DOI":"10.3390\/sym11111351","type":"journal-article","created":{"date-parts":[[2019,11,1]],"date-time":"2019-11-01T12:30:50Z","timestamp":1572611450000},"page":"1351","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Skewness of Maximum Likelihood Estimators in the Weibull Censored Data"],"prefix":"10.3390","volume":"11","author":[{"given":"Tiago M.","family":"Magalh\u00e3es","sequence":"first","affiliation":[{"name":"Department of Statistics, Institute of Exact Sciences, Federal University of Juiz de Fora, Juiz de Fora 36000-000, Brazil"}],"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":"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":[[2019,11,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1115\/1.4010337","article-title":"A statistical distribution function of wide applicability","volume":"18","author":"Weibull","year":"1951","journal-title":"J. Appl. Mech."},{"key":"ref_2","unstructured":"Kendall, M.G., and Stuart, A. (1977). The Advanced Theory of Statistic, Griffin. [4th ed.]."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2743","DOI":"10.1080\/03610929808832252","article-title":"Asymptotic skewness and the distribution of maximum likelihood estimators","volume":"27","author":"Bowman","year":"1998","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1317","DOI":"10.1081\/STA-100104747","article-title":"Skewness for parameters in generalized linear models","volume":"30","author":"Cordeiro","year":"2001","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4250","DOI":"10.1080\/03610926.2018.1490768","article-title":"Skewness of maximum likelihood estimators in the varying dispersion beta regression model","volume":"48","author":"Botter","year":"2019","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1080\/00949659708811796","article-title":"Improved likelihood ratio tests for exponential censored data","volume":"56","author":"Cordeiro","year":"1997","journal-title":"J. Stat. Comput. Sim."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/S0167-7152(99)00028-0","article-title":"Corrected score tests for exponential censored data","volume":"44","author":"Cordeiro","year":"1999","journal-title":"Stat. Probab. Lett."},{"key":"ref_8","unstructured":"Magalh\u00e3es, T.M., and Gallardo, D.I. (2019). Bartlett and Bartlett-type corrections for Weibull censored data. Stat. Oper. Res. 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Hung."},{"key":"ref_13","first-page":"7063","article-title":"Some properties of hypoexponential distribution with stabilizer constant","volume":"142","author":"Devianto","year":"2015","journal-title":"Appl. Math. Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/11\/1351\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:31:16Z","timestamp":1760189476000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/11\/1351"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,1]]},"references-count":13,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2019,11]]}},"alternative-id":["sym11111351"],"URL":"https:\/\/doi.org\/10.3390\/sym11111351","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,1]]}}}