A note on the characterization of the multivariate normal distribution

Metrika ◽  
1979 ◽  
Vol 26 (1) ◽  
pp. 25-30 ◽  
Author(s):  
Sh. Talwalker
Keyword(s):  
Normal Distribution ◽  
Multivariate Normal Distribution ◽  
Multivariate Normal

scholarly journals A Characterization and a Variational Inequality for the Multivariate Normal Distribution

1987 ◽  
Vol 43 (3) ◽  
pp. 366-374
Author(s):  
Wolfgang Stadje
Keyword(s):  
Variational Inequality ◽  
Normal Distribution ◽  
Multivariate Normal Distribution ◽  
Standard Normal Distribution ◽  
Multivariate Normal ◽  
Dimensional Linear Subspace ◽  
Symmetric Density ◽  
Rotationally Symmetric ◽  
Standard Normal

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.

A conditional characterization of the multivariate normal distribution

1994 ◽  
Vol 19 (4) ◽  
pp. 313-315 ◽  
Author(s):  
Barry C. Arnold ◽  
Enrique Castillo ◽  
Jose María Sarabia
Keyword(s):  
Normal Distribution ◽  
Multivariate Normal Distribution ◽  
Multivariate Normal
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