On the performance of the linear discriminant function for spherical distributions

A general integral expression is obtained for evaluating the performance of Fisher's linear discriminant function applied to spherical distributions (SD). Recurrence relations are given for certain special cases including the spherical gamma, Pearson VII, and generalized Laplace distributions. Some easily obtained upper and lower bounds for the probabilities of correct classification are shown to improve considerably the only available bounds, given by Haralick (Pattern Recognition 9, 1977).