Abstract
This paper extends previous work in discriminant analysis with von Mises-Fisher distributions (e. g., Morris and Laycock, Biometrika, 1974) to general dimension, allowing computation of misclassification probabilities. The main result is the probability distribution of the cosine transformation of a von Mises-Fisher distribution, that is, the random variable , where , satisfying , is a random direction with von Mises-Fisher distribution and , satisfying , is a fixed non-random direction. This transformation is of general interest in multivariate analysis, in particular it underlies discriminant analysis in both two-group and multiple group problem.
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