Some properties of multivariate extreme value distributions and multivariate tail equivalence
type: Item
instance of: scholarly article
title: Some properties of multivariate extreme value distributions and multivariate tail equivalence
zbMATH Open document ID: 0638.62049
DOI: 10.1007/BF02491496
author: Rinya Takahashi
published in: Annals of the Institute of Statistical Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Denote by H a k-dimensional extreme value distribution with marginal distribution \(H_ i(x)=\Lambda (x)=\exp (-e^{-x})\), \(x\in {\mathbb{R}}^ 1\). Then it is proved that \[ H({\mathfrak x})=\Lambda (x_ 1)...\Lambda (x_ k)\quad for\quad any\quad {\mathfrak x}=(x_ 1,...,x_ k)\in {\mathbb{R}}^ k, \] if and only if the equation holds for \({\mathfrak x}=(0,...,0)\). Next some multivariate extensions of the results by \textit{S. I. Resnick} [J. Appl. Probab. 8, 135-156 (1971; Zbl 0217.499)] on tail equivalence and asymptotic distributions of extremes are established.
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 4041067
zbMATH Keywords: multivariate extreme value distributions
zbMATH Keywords: multivariate extreme order statistics
zbMATH Keywords: tail equivalence
MaRDI profile type: Publication
cites work: Q5560061
cites work: Q5633348
cites work: Q4162318
cites work: Domains of attraction of multivariate extreme value distributions
cites work: Products of distribution functions attracted to extreme value laws
description: scientific article; zbMATH DE number 4041067