Pattern discrimination using ellipsoidally symmetric multivariate density functions

A brief review of ellipsoidally symmetric density functions is done. For the case of monotonic functional forms and distributions with common covariance matrices, a lower bound on the probability of correct classification is calculated in terms of either an incomplete beta or gamma integral, for a class of common functional forms. The lower bound is a monotonically increasing function of the Mahalanobis distance for all monotonic ellipsoidally symmetric forms.