On the Characterization of Certain Point Processes.

Abstract

It is well known that point process methods can be applied effectively to study certain types of problems in statistical extreme value theory. Consider a strictly stationary sequence of random variables (xi sub j) indexed by the set of integers I=Z. One can define a number of interesting point processes in one dimension by recording the positions where extreme values occur. For example, an extremal process typically is one that records the indices (properly normalized) at which record values of xi sub 1, xi or sub 2 occur, and an exceedance point process considered by Leadbetter consists of the set of points j.n: xi sub j > w sub n, where sub n is a suitable sequence of constants. For this type of processes, Poisson or compound Poisson convergence results can often be derived under suitable mixing conditions. Keywords: Weak convergence.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1987
Accession Number
ADA186427

Entities

People

  • Tailen Hsing

Organizations

  • University of North Carolina at Chapel Hill

Tags

DTIC Thesaurus Topics

  • Convergence
  • Data Science
  • Information Science
  • Insensitive Explosives
  • Intervals
  • New York
  • North Carolina
  • Order Statistics
  • Probability
  • Random Variables
  • Security
  • Sequences
  • Stationary
  • Statistics
  • Stochastic Processes
  • Universities
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Statistical inference.