Extremal Processes, Record Times and Strong Approximation.

Abstract

Given an i.i.d. sequence of random variables (r.v.'s) with continuous cumulative distribution function (CDF) F, the author presents a simple construction for the jump times of an extremal process on the same probability space which 'interpolate' the given record times. This gives another approach to the strong approximation of extremal processes as developed by Deheuvels (1981, 1982, 1983), and allows for a more detailed investigation of the relationship between the record times of the given sequence and the jump times of the extremal process. In particular, it is shown that the number S of surplus jump time points in (1, infinity) over the record times is approximately Poisson distributed with an exact mean of E(S) = 1 - C, C denoting Euler's constant. Keywords: Poisson approximation. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1985
Accession Number
ADA169972

Entities

People

  • Dietmar Pfeifer

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Construction
  • Distribution Functions
  • Intervals
  • Markov Chains
  • Markov Processes
  • North Carolina
  • Numbers
  • Probability
  • Random Variables
  • Real Numbers
  • Scientific Research
  • Sequences
  • Stochastic Processes
  • Structural Properties
  • Time Intervals

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Calculus or Mathematical Analysis
  • Regression Analysis.

Technology Areas

  • Space