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Two LDF characterizations of the normal as a spherical distribution

Author

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  • Cacoullos, Theophilos

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.

Suggested Citation

  • Cacoullos, Theophilos, 1992. "Two LDF characterizations of the normal as a spherical distribution," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 205-212, February.
    • Handle: RePEc:eee:jmvana:v:40:y:1992:i:2:p:205-212
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