Significance Points for Some Tests of Uniformity on the Sphere. Revision.

Abstract

Beran and Gine have proposed several omnibus tests for uniformity on the unit sphere in three dimensional Euclidean space. While several authors have contributed to providing approximate percentage points for the limiting distributions, no tables of the limiting distributions, percentage points thereof, or finite sample distributions or percentage points have been available. In this paper the authors fill this gap by: (1) finding the exact distributions of the statistics of Beran and Gine for n = 2; (2) presenting some percentage points for selected small and moderate sample sizes obtained by Monte-Carlo methods; (3) evaluating numerically the cumulative distribution functions and significance points of the limiting distributions via the Laguerre transform method.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1982
Accession Number
ADA128027

Entities

People

  • D. Petrondas
  • J. Keilson
  • J. Wellner
  • U. Sumita

Organizations

  • University of Rochester

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Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Air Force
  • Classification
  • Computer Science
  • Computers
  • Convolution
  • Data Science
  • Distribution Functions
  • Information Science
  • Knowledge Management
  • Monte Carlo Method
  • Probability
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  • Statistics
  • United States
  • Universities

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  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Statistical inference.
  • Systems Analysis and Design

Technology Areas

  • Space