TY - GEN

T1 - Estimation of the Weibull Tail Coefficient Through the Power Mean-of-Order-p

AU - Caeiro, Frederico

AU - Gomes, M. Ivette

AU - Henriques-Rodrigues, Lígia

N1 - Funding Information:
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT#
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00006%2F2020/PT#
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04674%2F2020/PT#
Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - Power mean-of-order-p

KW - Semi-parametric estimation

KW - Statistics of extremes

KW - Weibull tail coefficient

UR - http://www.scopus.com/inward/record.url?scp=85144397424&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-12766-3_4

DO - 10.1007/978-3-031-12766-3_4

M3 - Conference contribution

AN - SCOPUS:85144397424

SN - 978-3-031-12765-6

T3 - Springer Proceedings in Mathematics and Statistics

SP - 41

EP - 53

BT - Recent Developments in Statistics and Data Science

A2 - Bispo, Regina

A2 - Henriques-Rodrigues, Lígia

A2 - Alpizar-Jara, Russell

A2 - de Carvalho, Miguel

PB - Springer

CY - Springer, Cham

T2 - 25th Congress of the Portuguese Statistical Society, SPE 2021

Y2 - 13 October 2021 through 16 October 2021

ER -