Two LDF characterizations of the normal as a spherical distribution

Two optimal characteristic properties of the normal distribution are shown: (a) Of all the SNM (spherical scale normal mixtures) the normal with the same Mahalanobis distances between [Pi]i:SNM([mu]i) and [Pi]j:SNM([mu]j), i [not equal to] j, maximizes the probabilities of correct classification determined by a certain subclass of the LDF classification rules; (b) The class of LDF (linear discriminant function) rules is the admissible class for the discrimination problem with spherical population alternatives iff the spherical distribution is normal.Spherical distributions linear discriminant functions characterizations of normality spherical normal mixtures discriminatory power