DISPERSION ON A SPHERE: RAYLEIGH'S AND FISHER'S SOLUTIONS AND WATSON'S TEST FOR RANDOMNESS

Abstract

The distribution of R, the size of the resultant of N unit vectors randomly oriented in three dimensions, was solved by Rayleigh and in a quite different form by Fisher. These forms are proved equivalent. An improved significant table is given for a test for randomness, proposed by Watson, and based on this distribution. An approximate test is suggested and compared with the exact test. The power of the exact test against a given alternative distribution, suggested by Fisher, is used to calculate a table of sample sizes.

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Document Details

Document Type
Technical Report
Publication Date
Jul 02, 1962
Accession Number
AD0277744

Entities

Organizations

  • RTI International

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Contracts
  • Detection
  • Distribution Functions
  • Equations
  • Government Procurement
  • Governments
  • Integrals
  • Intervals
  • Military Research
  • Notation
  • Probability
  • Procurement
  • Random Walk
  • United States
  • United States Government
  • Universities

Fields of Study

  • Mathematics

Readers

  • Electromagnetic Wave Scattering and Antenna Radiation Engineering
  • Statistical inference.