{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:56:42Z","timestamp":1740110202955,"version":"3.37.3"},"reference-count":55,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2023,5,19]],"date-time":"2023-05-19T00:00:00Z","timestamp":1684454400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/00297\/2020","UIDP\/00297\/2020"],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2024,1]]},"DOI":"10.1016\/j.cam.2023.115347","type":"journal-article","created":{"date-parts":[[2023,5,24]],"date-time":"2023-05-24T15:25:07Z","timestamp":1684941907000},"page":"115347","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"C","title":["Reduced bias estimation of the shape parameter of the log-logistic distribution"],"prefix":"10.1016","volume":"436","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8628-7281","authenticated-orcid":false,"given":"Frederico","family":"Caeiro","sequence":"first","affiliation":[]},{"given":"Ayana","family":"Mateus","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"2","key":"10.1016\/j.cam.2023.115347_b1","doi-asserted-by":"crossref","first-page":"171","DOI":"10.2307\/1909287","article-title":"The graduation of income distributions","volume":"29","author":"Fisk","year":"1961","journal-title":"Econometrica"},{"issue":"1","key":"10.1016\/j.cam.2023.115347_b2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1742-4682-8-43","article-title":"A parametric method for cumulative incidence modeling with a new four-parameter log-logistic distribution","volume":"8","author":"Shayan","year":"2011","journal-title":"Theor. Biol. Med. Model."},{"issue":"1","key":"10.1016\/j.cam.2023.115347_b3","doi-asserted-by":"crossref","first-page":"91","DOI":"10.17159\/2413-3051\/2017\/v28i1a1530","article-title":"Quantifying South Africa\u2019s sulphur dioxide emission efficiency in coal-powered electricity generation by fitting the three-parameter log-logistic distribution","volume":"28","author":"Girmay","year":"2017","journal-title":"J. Energy South. Afr."},{"issue":"4","key":"10.1016\/j.cam.2023.115347_b4","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1002\/(SICI)1521-4036(199907)41:4<431::AID-BIMJ431>3.0.CO;2-U","article-title":"A study of log-logistic model in survival analysis","volume":"41","author":"Gupta","year":"1999","journal-title":"Biom. J."},{"issue":"2","key":"10.1016\/j.cam.2023.115347_b5","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1177\/0049124195024002002","article-title":"The log-logistic rate model: Two generalizations with an application to demographic data","volume":"24","author":"Br\u00fcederl","year":"1995","journal-title":"Sociol. Methods Res."},{"issue":"2","key":"10.1016\/j.cam.2023.115347_b6","first-page":"49","article-title":"Comparison of a modified log-logistic distribution with established models for tree height prediction","volume":"10","author":"Ogana","year":"2018","journal-title":"J. Res. For. Wildl. Environ."},{"issue":"3\u20134","key":"10.1016\/j.cam.2023.115347_b7","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/0022-1694(88)90015-7","article-title":"Log-logistic flood frequency analysis","volume":"98","author":"Ahmad","year":"1988","journal-title":"J. Hydrol."},{"issue":"1","key":"10.1016\/j.cam.2023.115347_b8","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1080\/02626660209492911","article-title":"A note on the applicability of log-gumbel and log-logistic probability distributions in hydrological analyses: I. Known pdf","volume":"47","author":"Rowinski","year":"2002","journal-title":"Hydrol. Sci. J."},{"issue":"3","key":"10.1016\/j.cam.2023.115347_b9","doi-asserted-by":"crossref","first-page":"463","DOI":"10.4153\/CMB-1967-045-7","article-title":"Exact distribution of the quotient of independent generalized Gamma variables","volume":"10","author":"Malik","year":"1967","journal-title":"Canad. Math. Bull."},{"issue":"2","key":"10.1016\/j.cam.2023.115347_b10","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1214\/aoms\/1177731607","article-title":"Cumulative frequency functions","volume":"13","author":"Burr","year":"1942","journal-title":"Ann. Math. Stat."},{"key":"10.1016\/j.cam.2023.115347_b11","first-page":"413","article-title":"A new model for personal income distribution: Specification and estimation","volume":"30","author":"Dagum","year":"1977","journal-title":"Econ. Appl."},{"issue":"12","key":"10.1016\/j.cam.2023.115347_b12","doi-asserted-by":"crossref","first-page":"3477","DOI":"10.1080\/03610928708829586","article-title":"Best linear unbiased estimation of location and scale parameters of the log-logistic distribution","volume":"16","author":"Balakrishnan","year":"1987","journal-title":"Comm. Statist. Theory Methods"},{"issue":"3","key":"10.1016\/j.cam.2023.115347_b13","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/BF01585596","article-title":"Parameter estimation for 3-parameter log-logistic distribution (LLD3) by pome","volume":"7","author":"Singh","year":"1993","journal-title":"Stoch. Hydrol. Hydraul."},{"issue":"3","key":"10.1016\/j.cam.2023.115347_b14","doi-asserted-by":"crossref","first-page":"647","DOI":"10.2307\/1913469","article-title":"Some generalized functions for the size distribution of income","volume":"52","author":"McDonald","year":"1984","journal-title":"Econometrica"},{"issue":"3","key":"10.1016\/j.cam.2023.115347_b15","doi-asserted-by":"crossref","first-page":"93","DOI":"10.5539\/ijsp.v10n3p93","article-title":"On the log-logistic distribution and its generalizations: A survey","volume":"10","author":"Muse","year":"2021","journal-title":"Int. J. Stat. Probab."},{"year":"2015","series-title":"Pareto Distributions","author":"Arnold","key":"10.1016\/j.cam.2023.115347_b16"},{"issue":"3","key":"10.1016\/j.cam.2023.115347_b17","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1016\/j.jhydrol.2006.01.014","article-title":"Fitting the log-logistic distribution by generalized moments","volume":"328","author":"Ashkar","year":"2006","journal-title":"J. Hydrol."},{"issue":"3","key":"10.1016\/j.cam.2023.115347_b18","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1007\/BF02762839","article-title":"Optimum group limits for estimation in scaled log-logistic distribution from a grouped data","volume":"46","author":"Kantam","year":"2005","journal-title":"Statist. Papers"},{"issue":"8","key":"10.1016\/j.cam.2023.115347_b19","first-page":"263","article-title":"Generalized least squares and weighted least squares estimation methods for distributional parameters","volume":"13","author":"Mert\u00a0Kantar","year":"2015","journal-title":"Revstat\u2013Stat. J."},{"issue":"8","key":"10.1016\/j.cam.2023.115347_b20","doi-asserted-by":"crossref","first-page":"2782","DOI":"10.1080\/03610918.2014.925925","article-title":"Objective Bayesian analysis for log-logistic distribution","volume":"45","author":"Abbas","year":"2016","journal-title":"Comm. Statist. Simulation Comput."},{"issue":"1","key":"10.1016\/j.cam.2023.115347_b21","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/s00180-017-0738-y","article-title":"Improved parameter estimation of the log-logistic distribution with applications","volume":"33","author":"Reath","year":"2017","journal-title":"Comput. Statist."},{"issue":"5","key":"10.1016\/j.cam.2023.115347_b22","doi-asserted-by":"crossref","first-page":"1875","DOI":"10.1007\/s00362-018-1011-3","article-title":"Maximum likelihood estimators of the parameters of the log-logistic distribution","volume":"61","author":"He","year":"2020","journal-title":"Statist. Papers"},{"key":"10.1016\/j.cam.2023.115347_b23","unstructured":"D. Abd El-Rahman, M. El\u00a0Genidy, Three Parameters Estimation of Log-Logistic Distribution Using Algorithm of Percentile Roots, in: The 54th Annual Conference on Statistics, Computer Science and Operation Research, 2019."},{"issue":"4","key":"10.1016\/j.cam.2023.115347_b24","first-page":"429","article-title":"Parameter estimation for the log-logistic distribution based on order statistics","volume":"16","author":"Ahsanullah","year":"2018","journal-title":"Revstat \u2013 Stat. J."},{"key":"10.1016\/j.cam.2023.115347_b25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2022\/8400130","article-title":"Improved shape parameter estimation for the three-parameter log-logistic distribution","volume":"2022","author":"Mateus","year":"2022","journal-title":"Comput. Math. Methods"},{"issue":"1","key":"10.1016\/j.cam.2023.115347_b26","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1111\/j.2517-6161.1982.tb01183.x","article-title":"On some simple estimates of an exponent of regular variation","volume":"44","author":"Hall","year":"1982","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"key":"10.1016\/j.cam.2023.115347_b27","series-title":"Stochastic Musings: Perspectives from the Pioneers of the Late 20th Century","first-page":"141","article-title":"Extreme value index estimators and smoothing alternatives: A critical review","author":"Panaretos","year":"2003"},{"key":"10.1016\/j.cam.2023.115347_b28","series-title":"Extreme Events in Finance","first-page":"97","article-title":"Estimation of the extreme value index","author":"Beirlant","year":"2016"},{"issue":"3","key":"10.1016\/j.cam.2023.115347_b29","first-page":"245","article-title":"A review of more than one hundred Pareto-tail index estimators","volume":"80","author":"Fedotenkov","year":"2020","journal-title":"Statistica"},{"issue":"1","key":"10.1016\/j.cam.2023.115347_b30","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1080\/03610926.2020.1746970","article-title":"On the comparison of several classical estimators of the extreme value index","volume":"51","author":"Cabral","year":"2022","journal-title":"Comm. Statist. Theory Methods"},{"issue":"5","key":"10.1016\/j.cam.2023.115347_b31","doi-asserted-by":"crossref","first-page":"1163","DOI":"10.1214\/aos\/1176343247","article-title":"A simple general approach to inference about the tail of a distribution","volume":"3","author":"Hill","year":"1975","journal-title":"Ann. Statist."},{"issue":"4","key":"10.1016\/j.cam.2023.115347_b32","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1081\/SAC-120023875","article-title":"How can non-invariant statistics work in our benefit in the semi-parametric estimation of parameters of rare events","volume":"32","author":"Gomes","year":"2003","journal-title":"Comm. Statist. Simulation Comput."},{"issue":"1","key":"10.1016\/j.cam.2023.115347_b33","first-page":"1","article-title":"Minimum-variance reduced-bias tail index and high quantile estimation","volume":"6","author":"Caeiro","year":"2008","journal-title":"Revstat \u2013 Stat. J."},{"issue":"5","key":"10.1016\/j.cam.2023.115347_b34","doi-asserted-by":"crossref","first-page":"1166","DOI":"10.1080\/03610926.2018.1425448","article-title":"A location-invariant non-positive moment-type estimator of the extreme value index","volume":"48","author":"Liu","year":"2018","journal-title":"Comm. Statist. Theory Methods"},{"issue":"3","key":"10.1016\/j.cam.2023.115347_b35","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1023\/A:1015226104400","article-title":"A location invariant hill-type estimator","volume":"4","author":"Fraga\u00a0Alves","year":"2001","journal-title":"Extremes"},{"issue":"3","key":"10.1016\/j.cam.2023.115347_b36","first-page":"227","article-title":"Peaks over random threshold methodology for tail index and high quantile estimation","volume":"4","author":"Ara\u00fajo\u00a0Santos","year":"2006","journal-title":"Revstat \u2013 Stat. J."},{"issue":"4","key":"10.1016\/j.cam.2023.115347_b37","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1080\/03610929608831735","article-title":"Refined pickands estimators with bias correction","volume":"25","author":"Drees","year":"1996","journal-title":"Comm. Statist. Theory Methods"},{"issue":"2","key":"10.1016\/j.cam.2023.115347_b38","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/S0167-7152(97)00160-0","article-title":"Asymptotically unbiased estimators for the extreme-value index","volume":"38","author":"Peng","year":"1998","journal-title":"Statist. Probab. Lett."},{"issue":"1","key":"10.1016\/j.cam.2023.115347_b39","first-page":"1","article-title":"An overview and open research topics in statistics of univariate extremes","volume":"10","author":"Beirlant","year":"2012","journal-title":"Revstat \u2013 Stat. J."},{"issue":"2","key":"10.1016\/j.cam.2023.115347_b40","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1111\/insr.12058","article-title":"Extreme value theory and statistics of univariate extremes: a review","volume":"83","author":"Gomes","year":"2015","journal-title":"Internat. Statist. Rev."},{"year":"2004","series-title":"Statistics of Extremes: Theory and Applications","author":"Beirlant","key":"10.1016\/j.cam.2023.115347_b41"},{"issue":"3","key":"10.1016\/j.cam.2023.115347_b42","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1023\/A:1011470010228","article-title":"Alternatives to a semi-parametric estimator of parameters of rare events\u2013the jackknife methodology","volume":"3","author":"Gomes","year":"2000","journal-title":"Extremes"},{"issue":"4","key":"10.1016\/j.cam.2023.115347_b43","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1007\/s10687-016-0256-2","article-title":"Weak properties and robustness of t-hill estimators","volume":"19","author":"Jordanova","year":"2016","journal-title":"Extremes"},{"issue":"4","key":"10.1016\/j.cam.2023.115347_b44","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1080\/03610929608831727","article-title":"The method of moments ratio estimator for the tail shape parameter","volume":"25","author":"Danielsson","year":"1996","journal-title":"Comm. Statist. Theory Methods"},{"issue":"3","key":"10.1016\/j.cam.2023.115347_b45","first-page":"281","article-title":"A couple of non reduced bias generalized means in extreme value theory: An asymptotic comparison","volume":"18","author":"Penalva","year":"2020","journal-title":"Revstat\u2013Stat. J."},{"issue":"13\u201315","key":"10.1016\/j.cam.2023.115347_b46","doi-asserted-by":"crossref","first-page":"2825","DOI":"10.1080\/02664763.2019.1694871","article-title":"Lehmer\u2019s mean-of-order-p extreme value index estimation: a simulation study and applications","volume":"47","author":"Penalva","year":"2020","journal-title":"J. Appl. Stat."},{"issue":"2","key":"10.1016\/j.cam.2023.115347_b47","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1111\/jfr3.12296","article-title":"Technical note: comparison of methods for threshold selection for extreme sea levels","volume":"11","author":"Caballero-Megido","year":"2017","journal-title":"J. Flood Risk Manage."},{"key":"10.1016\/j.cam.2023.115347_b48","series-title":"Extreme Value Modeling and Risk Analysis","first-page":"69","article-title":"Threshold selection in extreme value analysis","author":"Caeiro","year":"2015"},{"issue":"4","key":"10.1016\/j.cam.2023.115347_b49","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1007\/s10687-021-00405-7","article-title":"Threshold selection in univariate extreme value analysis","volume":"24","author":"Schneider","year":"2021","journal-title":"Extremes"},{"year":"1995","series-title":"Exponential Distribution: Theory, Methods and Applications","author":"Balakrishnan","key":"10.1016\/j.cam.2023.115347_b50"},{"issue":"2","key":"10.1016\/j.cam.2023.115347_b51","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1081\/STA-120028371","article-title":"A hill type estimator of the Weibull tail-coefficient","volume":"33","author":"Girard","year":"2004","journal-title":"Comm. Statist. Theory Methods"},{"year":"2022","series-title":"R: A Language and Environment for Statistical Computing","author":"R Core Team","key":"10.1016\/j.cam.2023.115347_b52"},{"year":"1991","series-title":"Repeat variability in instantaneously released heavy gas clouds-some wind tunnel model experiments","author":"Hall","key":"10.1016\/j.cam.2023.115347_b53"},{"issue":"1","key":"10.1016\/j.cam.2023.115347_b54","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1063\/1.4897792","article-title":"An r implementation of several randomness tests","volume":"1618","author":"Mateus","year":"2014","journal-title":"AIP Conf. Proc."},{"issue":"1","key":"10.1016\/j.cam.2023.115347_b55","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1111\/j.1467-842X.2006.00426.x","article-title":"A new family of non-negative distributions","volume":"48","author":"Hankin","year":"2006","journal-title":"Aust. N. Z. J. Stat."}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042723002911?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042723002911?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2024,10,21]],"date-time":"2024-10-21T00:59:22Z","timestamp":1729472362000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042723002911"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1]]},"references-count":55,"alternative-id":["S0377042723002911"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2023.115347","relation":{},"ISSN":["0377-0427"],"issn-type":[{"type":"print","value":"0377-0427"}],"subject":[],"published":{"date-parts":[[2024,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Reduced bias estimation of the shape parameter of the log-logistic distribution","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2023.115347","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2023 The Author(s). Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"115347"}}