Two LDF characterizations of the normal as a spherical distribution

Theophilos Cacoullos

Journal of Multivariate Analysis, 1992, vol. 40, issue 2, 205-212

Abstract: 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.

Keywords: Spherical; distributions; linear; discriminant; functions; characterizations; of; normality; spherical; normal; mixtures; discriminatory; power (search for similar items in EconPapers)
Date: 1992
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