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A Characterization and a Variational Inequality for the Multivariate Normal Distribution
Published online by Cambridge University Press: 09 April 2009
Extract
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.
MSC classification
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 43 , Issue 3 , December 1987 , pp. 366 - 374
- Copyright
- Copyright © Australian Mathematical Society 1987