ON DISTRIBUTION FUNCTION - MOMENT RELATIONSHIPS IN A STATIONARY POINT PROCESS,

Abstract

Let G sub n (t) denote the distribution function for the time to the n-th event in a stationary regular point process, and F sub n (t) the corresponding distribution function, conditional on an event having occurred 'at' t = 0. (i.e., F sub n (t) represents the distribution of the time from an 'arbitrary event' to the n-th subsequent event). Let N(o, t) denote the number of events in (o, t). Relationships between the distribution functions G sub n, F sub n, and the moments (unconditional and conditional) of N(o, t) are obtained. Specifically, series are given for G sub n (t) in terms of factorial moments of N(o, t), and for F sub n (t) in terms of such moments, conditional on the occurrence of an event 'at' t = 0. (Author)

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1969
Accession Number
AD0683322

Entities

People

  • M. Ross Leadbetter
  • Robert J. Serfling

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Distribution Functions
  • Functions (Mathematics)
  • Stationary

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Regression Analysis.