On the Exceedance Point Process for a Stationary Sequence.

Abstract

It is known that the exceedance points of a high level by a stationary sequence are asymptotically Poisson as the level increases, under appropriate long range and local dependence conditions. When the local dependence conditions are relaxed, clustering of exceedances may occur, based on Poisson positions for the clusters. In this paper a detailed analysis of the exceedance point process is given, and show that, under wide conditions, any limiting point process for exceedances is necessarily compound Poisson. Sufficient conditions are also given for the existence of such a limit. The limiting distributions of extreme order statistics are derived as corollaries. Keywords include: Extreme values; stochastic processes; exceedances; point processes.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1985
Accession Number
ADA152827

Entities

People

  • M. Ross Leadbetter
  • T. Hsing

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Classification
  • Clustering
  • Convergence
  • Distribution Functions
  • North Carolina
  • Order Statistics
  • Probability
  • Random Variables
  • Scientific Research
  • Security
  • Sequences
  • Stationary
  • Statistics
  • Stochastic Processes
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Materials Science and Engineering.
  • Statistical inference.