A Characterization and a Variational Inequality for the Multivariate Normal Distribution

Journal of the Australian Mathematical Society

Wolfgang Stadje¹ 

关键词: 62 H 05;   

DOI  :  10.1017/S1446788700029645

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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.

【 授权许可】

Unknown