Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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A Test Based on Euler Angles of a Rotationally Symmetric Spherical Distribution

  • Published : 1999.04.30
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Abstract

For a orientation-shift model supported on the unit sphere, Euler angles are the conventional measure to parametrize orientation-shifts. The essential role which is played by rotationally symmetry of an underlying distribution is reviewed. In this paper we propose the inference procedure based on Euler angles for the rotationally symmetric spherical distribution. The likelihood ratio test(LRT) based on the Euler angles is worked out. The asymptotic distribution of the test under the null hypotheses and certain contiguous alternatives is obtained.

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References

  1. Austral. J. Statist. v.28 Goodness-of-fit and discordancy tests for samples from the Watson distribution on the sphere Best, D. J.;Fisher, N. I.
  2. Ann. Statist. v.2 An antipodally symmetric distribution on the sphere Bingham, C.
  3. Austral. J. Statist. v.6 Goodness-of-fit tests for Fisher's distribution on the sphere Fisher, N. I.;Best, D. J.
  4. Statistical analysis of spherical data Fisher, N. I.;Lewis, T.;Embleton, B. J. J.
  5. Ph.D. Thesis. Univ. of California Orientation-shift Model on the Sphere
  6. J. R. Statist. Soc. B v.37 Statistics of directional data(with discussion) Marida, K. V.
  7. Statistics on Spheres Watson, G. S.