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Title: Estimation of the Weibull tail coefficient through the power-mean-of-order p
Authors: Caeiro, Frederico
Gomes, Maria Ivette
Henriques-Rodrigues, Lígia
Editors: Bispo, Regina
Henriques-Rodrigues, Lígia
Alpizar-Jara, Russell
de Carvalho, Miguel
Keywords: Power mean-of-order-p Semi-parametric estimation Statistics of extremes
Semi-parametric estimation
Statistics of extremes
Weibull tail coefficient
Issue Date: 29-Nov-2022
Publisher: Springer
Citation: Caeiro, F., Gomes, M.I., Henriques-Rodrigues, L. (2022). Estimation of the Weibull Tail Coefficient Through the Power Mean-of-Order-p. In: Bispo, R., Henriques-Rodrigues, L., Alpizar-Jara, R., de Carvalho, M. (eds) Recent Developments in Statistics and Data Science. SPE 2021. Springer Proceedings in Mathematics & Statistics, vol 398. Springer, Cham.
Abstract: The Weibull tail coefficient (WTC) is the parameter θ θ in a right-tail function of the type F¯:=1−F 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 (MOp) 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.
ISBN: 978-3-031-12765-6
Type: bookPart
Appears in Collections:CIMA - Publicações - Capítulos de Livros

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