The distribution $\Psi(\mathbf{x}; Z, M) = \operatorname{const}. \exp(\mathrm{tr} (ZM^T \mathbf{xx}^T M))$ on the unit sphere in three-space is discussed. It is parametrized by the diagonal shape and concentration matrix $Z$ and the orthogonal orientation matrix $M. \Psi$ is applicable in the statistical analysis of measurements of random undirected axes. Exact and asymptotic sampling distributions are derived. Maximum likelihood estimators for $Z$ and $M$ are found and their asymptotic properties elucidated. Inference procedures, including tests for isotropy and circular symmetry, are proposed. The application of $\Psi$ is illustrated by a numerical example.
Publié le : 1974-11-14
Classification:
Distribution on sphere,
distribution of directions,
distribution of axes,
test of isotropy,
test of circularity,
hypergeometric functions,
62E99,
33A30,
62F05,
62F10
@article{1176342874,
author = {Bingham, Christopher},
title = {An Antipodally Symmetric Distribution on the Sphere},
journal = {Ann. Statist.},
volume = {2},
number = {1},
year = {1974},
pages = { 1201-1225},
language = {en},
url = {http://dml.mathdoc.fr/item/1176342874}
}
Bingham, Christopher. An Antipodally Symmetric Distribution on the Sphere. Ann. Statist., Tome 2 (1974) no. 1, pp. 1201-1225. http://gdmltest.u-ga.fr/item/1176342874/