A note on Gaussian distributions in ℝn

Given any finite set of ( n  − 1)-dimensional subspaces of ℝ n we give examples of nonGaussian probability measures in ℝ n whose marginal distribution in each subspace from is Gaussian. However, if is an infinite family of such ( n  − 1)-dimensional subspaces then such a nonGaussian probability meas...

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Bibliographic Details
Published inProceedings of the Indian Academy of Sciences. Mathematical sciences Vol. 122; no. 4; pp. 635 - 644
Main Authors MANJUNATH, B G, PARTHASARATHY, K R
Format Journal Article
LanguageEnglish
Published India Springer-Verlag 2012
Subjects
Mathematics
Mathematics and Statistics
Gaussian distribution
Hermite polynomial
homogeneous polynomial
characteristic function
linear functionals
nonunimodality
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Summary:Given any finite set of ( n  − 1)-dimensional subspaces of ℝ n we give examples of nonGaussian probability measures in ℝ n whose marginal distribution in each subspace from is Gaussian. However, if is an infinite family of such ( n  − 1)-dimensional subspaces then such a nonGaussian probability measure in ℝ n does not exist.
ISSN:0253-4142
0973-7685
DOI:10.1007/s12044-012-0099-y