{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T11:54:50Z","timestamp":1778068490475,"version":"3.51.4"},"reference-count":39,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,2,13]],"date-time":"2022-02-13T00:00:00Z","timestamp":1644710400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/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":["UIDP\/00297\/2020"],"award-info":[{"award-number":["UIDP\/00297\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/00297\/2020"],"award-info":[{"award-number":["UIDB\/00297\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods"],"published-print":{"date-parts":[[2022,2,13]]},"abstract":"<jats:p>The log-logistic distribution is widely used in different fields of study such as survival analysis, hydrology, insurance, and economics. Recently, Ahsanullah and Alzaatreh studied the best linear unbiased estimators for the location and the scale parameters of the three-parameter log-logistic model. The same authors also propose a shift-invariant Hill estimator for the unknown shape parameter. In this work, we propose a new estimation method for the shape parameter. We derive its nondegenerate asymptotic behaviour and analyse its finite sample performance through a Monte Carlo simulation study. To have precise estimates, we present a method for selecting the threshold. To illustrate the improvement achieved, efficiency comparisons are also provided.<\/jats:p>","DOI":"10.1155\/2022\/8400130","type":"journal-article","created":{"date-parts":[[2022,2,13]],"date-time":"2022-02-13T23:05:20Z","timestamp":1644793520000},"page":"1-13","source":"Crossref","is-referenced-by-count":5,"title":["Improved Shape Parameter Estimation for the Three-Parameter Log-Logistic Distribution"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5630-3321","authenticated-orcid":true,"given":"Ayana","family":"Mateus","sequence":"first","affiliation":[{"name":"NOVA School of Science and Technology (FCT NOVA), NOVA University Lisbon, Caparica, Portugal"},{"name":"Center for Mathematics and Applications (CMA), FCT NOVA and Department of Mathematics, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8628-7281","authenticated-orcid":true,"given":"Frederico","family":"Caeiro","sequence":"additional","affiliation":[{"name":"NOVA School of Science and Technology (FCT NOVA), NOVA University Lisbon, Caparica, Portugal"},{"name":"Center for Mathematics and Applications (CMA), FCT NOVA and Department of Mathematics, Portugal"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1080\/03610928708829586"},{"key":"2","article-title":"Pareto distributions","volume-title":"Monographs on Statistics and Applied Probability Chapman and Hall\/CRC","author":"B. 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