High level exceedances in stationary sequences with extremal index
type: Item
instance of: scholarly article
title: High level exceedances in stationary sequences with extremal index
zbMATH Open document ID: 0657.60027
DOI: 10.1016/0304-4149(88)90073-7
published in: Stochastic Processes and their Applications
publication date: 1988-01-01T00:00:00Z
review text: Let \(\{\xi_ n\}\) be a stationary sequence satisfying an analogue of Leadbetter's \(D(u_ n)\) condition and possessing extremal index \(\theta\), \(0<\theta \leq 1\). Denote by \(S_ n\) the number of exceedances of a level \(u_ n\) by \(\xi_ 1,...,\xi_ n\), i.e., the number of i, \(1\leq i\leq n\), such that \(\xi_ i>u_ n.\) The author proves that the limit laws of \(S_ n\) is of the compound Poisson type and specifies the parameters. She also determines the joint limit laws for exceedances of multiple levels, and consequently, for finite numbers of upper order statistics.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 4074066
zbMATH Keywords: number of exceedances
zbMATH Keywords: compound Poisson
zbMATH Keywords: limit laws for exceedances of multiple levels
zbMATH Keywords: order statistics
author: Maria Teresa Alpuim
reviewed by: Wiesław Dziubdziela
MaRDI profile type: Publication
full work available at URL: 0304-4149(88)90073-7
OpenAlex ID: W2042370445
cites work: Limit laws for kth order statistics from strong-mixing processes
cites work: On the exceedance point process for a stationary sequence
cites work: On extreme values in stationary sequences
cites work: Extremes and local dependence in stationary sequences
cites work: Extremes and related properties of random sequences and processes
cites work: Extreme values for stationary and Markov sequences
description: scientific article; zbMATH DE number 4074066