Covering the Circle with Random Arcs of Random Sizes.

Abstract

Consider the random uniform placement of a finite number of arcs on the circle, where the arc lengths are sampled from a distribution on (0,1). We provide exact formulae for the probability that the circle is completely covered and for the distribution of the number of uncovered gaps, extending Stevens' (1939) formulae for the case of fixed equal arc lengths. A special class of arc length distributions is considered, and exact probabilities of coverage are tabulated for the uniform distribution on (0,1). Some asymptotic results for the number of gaps are also given. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1980
Accession Number
ADA092659

Entities

People

  • Andrew F. Siegel
  • Lars Holst

Organizations

  • Princeton University

Tags

DTIC Thesaurus Topics

  • Asymptotic Series
  • Coverings
  • Distribution Functions
  • Harmonic Analysis
  • Mathematics
  • Military Research
  • Probability
  • Probability Distributions
  • Random Variables
  • Statistics
  • Universities

Fields of Study

  • Mathematics

Readers

  • Statistical inference.