Large Sample Theory of the Fisher-Von Mises Distribution.

Abstract

The Fisher-von-Mises distribution has probability density proportional to exp kappa micron prime x where x and microns are points on the surface of the unit ball in q dimensions. Kappa greater than or equal to 0 is a concentration parameter and micron the 'mean' or modal direction. This paper makes a self-contained study of estimation and testing problems when the sample sizes are large. Earlier work used approximations based on eta finite and kappa large. Some of these results are shown to be true for all kappa if eta yields infinity. New tests are given by comparing the kappa's and the micron's of different populations; the latter tests do not assume that all populations have the same kappa's. Further, power functions are given for the proposed tests. Because the random vectors are of unit length we may expect these asymptotic distributions to be accurate approximations even with quite small sample sizes. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1981
Accession Number
ADA117515

Entities

People

  • Geoffrey S. Watson

Organizations

  • Princeton University

Tags

DTIC Thesaurus Topics

  • Probability

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Optical Physics and Photonics.
  • Regression Analysis.