Note(s): Characterization of the p-generalized normal distribution

  • Authors:
  • Fabian Sinz;Sebastian Gerwinn;Matthias Bethge

  • Affiliations:
  • Max Planck Institute for Biological Cybernetics, Spemannstraíe 41, 72076 Tübingen, Germany;Max Planck Institute for Biological Cybernetics, Spemannstraíe 41, 72076 Tübingen, Germany;Max Planck Institute for Biological Cybernetics, Spemannstraíe 41, 72076 Tübingen, Germany

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2009

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Abstract

It is a well known fact that invariance under the orthogonal group and marginal independence uniquely characterizes the isotropic normal distribution. Here, a similar characterization is provided for the more general class of differentiable bounded L"p-spherically symmetric distributions: Every factorial distribution in this class is necessarily p-generalized normal.