Asymptotic Coverage Distributions on the Circle

Abstract

Let n arcs, each of length G sub N, be placed uniformly at random on the circumference of a circle. If the arc length sequence is chosen so that the coverage probability remains constant, then as n becomes large, a limiting noncentral chi-square distribution with zero degrees of freedom is obtained for the uncovered proportion of the circle. The case of proportionately smaller arcs is also treated, and a limiting normal distribution is found. Applications include immunology, genetics, and time series analysis.

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Document Details

Document Type
Technical Report
Publication Date
Apr 11, 1978
Accession Number
ADA054783

Entities

People

  • Andrew F. Siegel

Organizations

  • Stanford University

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Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Allergy And Immunology
  • Applied Mathematics
  • Contracts
  • Distribution Functions
  • Genetics
  • Identities
  • Mathematics
  • Military Research
  • Normal Distribution
  • Probability
  • Random Variables
  • Security
  • Sequences
  • Statistics
  • Time Series Analysis
  • United States

Fields of Study

  • Mathematics

Readers

  • Geodesy
  • Regression Analysis.

Technology Areas

  • Biotechnology