A Note on Gaussian Distributions in $mathbb{R}^n$

Proceedings Mathematical Sciences

B G Manjunath²  K R Parthasarathy¹ 

[1] $$;Indian Statistical Institute, Delhi Centre, , S. J. S. Sansanwal Marg, New Delhi 0 0, India$$

关键词: Gaussian distribution;    characteristic function;    homogeneous polynomial;    linear functionals;    nonunimodality;    Hermite polynomial.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Given any finite set $mathcal{F}$ of (𝑛-1)-dimensional subspaces of $mathbb{R}^n$ we give examples of nonGaussian probability measures in $mathbb{R}^n$ whose marginal distribution in each subspace from $mathcal{F}$ is Gaussian. However, if $mathcal{F}$ is an infinite family of such (𝑛-1)-dimensional subspaces then such a nonGaussian probability measure in $mathbb{R}^n$ does not exist.

【 授权许可】

Unknown