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Biometrika 1987 74(3):579-589; doi:10.1093/biomet/74.3.579
© 1987 by Biometrika Trust
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Statistical analysis for the angular central Gaussian distribution on the sphere

DAVID E. TYLER

Department of Statistics, Rutgers University New Brunswick, New Jersey 08903, U.S.A.

The angular central Gaussian distribution is an alternative to the Bingham distribution for modeling antipodal symmetric directional data. In this paper the statistical theory for the angular central Gaussian model is presented. Some topics treated are maximum likelihood estimation of the parameters, testing for uniformity and circularity, and principal components analysis. Comparisons to methods based upon the sample second moments are made via an example.

Key Words: Axial data • Bingham distribution • Bipolar distribution • Directional data • Girdle distribution • Principal component • Principal direction • Test for circularity • Test for uniformity


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