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 -