Random Arcs on the Circle

Abstract

Place n arcs of equal lengths randomly on the circumference of a circle, and let C denote the proportion covered. The moments of C (moments of coverage) are found by solving a recursive integral equation, and a formula is derived for the cumulative distribution function. The asymptotic distribution of C for large n is explored, and is shown to be related to the exponential distribution.

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Document Details

Document Type
Technical Report
Publication Date
Jul 26, 1977
Accession Number
ADA044901

Entities

People

  • Andrew F. Siegel

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Distribution Functions
  • Equations
  • Integral Equations
  • Integrals
  • Mathematical Analysis
  • Method Of Moments
  • Military Research
  • Probability
  • Probability Distributions
  • Random Variables
  • Statistics
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Computational Modeling and Simulation
  • Graph Algorithms and Convex Optimization.