A Characterization of Deviation from Normality Under Certain Moment Assumptions

1966 ◽  
Vol 9 (4) ◽  
pp. 509-514
Author(s):  
W.R. McGillivray ◽  
C.L. Kaller
Keyword(s):  
Distribution Function ◽  
Normal Distribution ◽  
Standard Normal Distribution ◽  
Standard Normal ◽  
Image Position

If Fn is the distribution function of a distribution n with moments up to order n equal to those of the standard normal distribution, then from Kendall and Stuart [1, p.87],

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.

scholarly journals Normality of some p—adic product expansions

1990 ◽  
Vol 49 (2) ◽  
pp. 258-263
Author(s):  
Arnold Knopfmacher ◽  
John Knopfmacher
Keyword(s):  
Normal Distribution ◽  
Haar Measure ◽  
Distribution Functions ◽  
Standard Normal Distribution ◽  
Standard Normal ◽  
Image Position ◽  
Almost All

AbstractWe consider two unique products for a given p—adic integer x with leading coefficient 1, where anbn ∈ {0, 1,… p − 1}. It is shown that, for almost all such x relative to Haar measure on the p—adic integers, the sequences (an), (bn) are normal to base p, and have standard normal distribution functions.

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