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A Characterization and a Variational Inequality for the Multivariate Normal Distribution

Published online by Cambridge University Press:  09 April 2009

Wolfgang Stadje
Affiliation:
Fachbereich Mathematik Universitat OsnabriickAlbrechtstrasse 28 West, Germany
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Various generalizations of the Maxwell characterization of the multivariate standard normal distribution are derived. For example the following is proved: If for a k-dimensional random vector X there exists an n ∈ {l, …, k − l} such that for each n-dimensional linear subspace H Rk the projections of X on H and H are independent, X is normal. If X has a rotationally symmetric density and its projection on some H has a density of the same functional form, X is normal. Finally we give a variational inequality for the multivariate normal distribution which resembles the isoperimetric inequality for the surface measure on the sphere.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1987

References

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