Extreme value theory for suprema of random variables with regularly varying tail probabilities
type: Item
instance of: scholarly article
title: Extreme value theory for suprema of random variables with regularly varying tail probabilities
zbMATH Open document ID: 0598.60026
DOI: 10.1016/0304-4149(86)90113-4
author: Tailen Hsing
published in: Stochastic Processes and their Applications
publication date: 1986-01-01T00:00:00Z
review text: Let \(\{z_ i\}\) (i\(\in I)\) be a sequence of i.i.d. random variables with d.f. F(x) where \(1-F(x)=x^{-\alpha}L(x)\), L(x) slowly varying. Among other less important results it is shown that: a) Prob\(\{\) \(\sup_{i}c_ iz_ i>x\}\sim x^{-\alpha}L(x)\sum c_ i^{\alpha}\) as \(x\to +\infty\) under some restrictions; b) the two dimensional point process \(\{(j/n,(a_ nX_ i)^{- \alpha}\}\) with \(X_ n=\sup_{i}c_ iZ_{n-i}\) is shown to have a limit.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 3965082
zbMATH Keywords: extreme value
zbMATH Keywords: regular variation
zbMATH Keywords: weak limits
MaRDI profile type: Publication
full work available at URL: 0304-4149(86)90113-4
OpenAlex ID: W2072764321
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description: scientific article; zbMATH DE number 3965082