A note on Gaussian distributions in ℝn
A note on Gaussian distributions in ℝn
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Date
2012-01-01
Authors
Manjunath, B. G.
Parthasarathy, K. R.
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Abstract
Given any finite set F of (n - 1)-dimensional subspaces of Rn we give examples of nonGaussian probability measures in R{double-struck}n whose marginal distribution in each subspace from F is Gaussian. However, if F is an infinite family of such (n - 1)- dimensional subspaces then such a nonGaussian probability measure in R{double-struck}n does not exist. ©Indian Academy of Sciences.
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Keywords
Characteristic function,
Gaussian distribution,
Hermite polynomial,
Homogeneous polynomial,
Linear functionals,
Nonunimodality
Citation
Proceedings of the Indian Academy of Sciences: Mathematical Sciences. v.122(4)