A Characterization and a Variational Inequality for the Multivariate Normal Distribution
1987 ◽
Vol 43
(3)
◽
pp. 366-374
Keyword(s):
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.
1962 ◽
Vol 33
(2)
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pp. 533-541
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2016 ◽
Vol 30
(2)
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pp. 141-152
1994 ◽
Vol 19
(4)
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pp. 313-315
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1977 ◽
Vol 6
(2)
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pp. 135-140
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2004 ◽
Vol 56
(2)
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pp. 361-367
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1971 ◽
Vol 42
(2)
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pp. 824-827
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