Estimation of the Weibull Tail Coefficient Through the Power Mean-of-Order-p

Frederico Caeiro, M. Ivette Gomes, Lígia Henriques-Rodrigues

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)


The Weibull tail coefficient (WTC) is the parameter θ in a right-tail function of the type F¯ : = 1 - F, such that H: = - ln F¯ is a regularly varying function at infinity with an index of regular variation equal to θ∈ R+. In a context of extreme value theory for maxima, it is possible to prove that we have an extreme value index (EVI) ξ= 0, but usually a very slow rate of convergence. Most of the recent WTC-estimators are proportional to the class of Hill EVI-estimators, the average of the log-excesses associated with the k upper order statistics, 1 ≤ k< n. The interesting performance of EVI-estimators based on generalized means leads us to base the WTC-estimation on the power mean-of-order-p (MO p ) EVI-estimators. Consistency of the WTC-estimators is discussed and their performance, for finite samples, is illustrated through a small-scale Monte Carlo simulation study.

Original languageEnglish
Title of host publicationRecent Developments in Statistics and Data Science
Subtitle of host publication SPE2021
EditorsRegina Bispo, Lígia Henriques-Rodrigues, Russell Alpizar-Jara, Miguel de Carvalho
Place of PublicationSpringer, Cham
Number of pages13
ISBN (Electronic)978-3-031-12766-3
ISBN (Print)978-3-031-12765-6
Publication statusPublished - 2022
Event25th Congress of the Portuguese Statistical Society, SPE 2021 - Virtual, Online
Duration: 13 Oct 202116 Oct 2021

Publication series

NameSpringer Proceedings in Mathematics and Statistics
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017


Conference25th Congress of the Portuguese Statistical Society, SPE 2021
CityVirtual, Online


  • Power mean-of-order-p
  • Semi-parametric estimation
  • Statistics of extremes
  • Weibull tail coefficient


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