Spherical uniformity and some characterizations of the Cauchy distribution
Ibrahim Salama,Pranab Kumar Sen +1 more
TLDR
In this article, a fixed line L (in Rn) and a uniform distribution of points (c) on the unit sphere, L(tc), the point of intersection of L and the hyperplane P · c = 0, is shown to have a Cauchy distribution.About:
This article is published in Journal of Multivariate Analysis.The article was published on 1992-05-01 and is currently open access. It has received 0 citations till now. The article focuses on the topics: Cauchy distribution & Unit sphere.read more
References
More filters
Journal ArticleDOI
On the theory of elliptically contoured distributions
TL;DR: The theory of elliptically contoured distributions is presented in an unrestricted setting, with no moment restrictions or assumptions of absolute continuity as mentioned in this paper, where the distributions are defined parametrically through their characteristic functions and then studied primarily through the use of stochastic representations which naturally follow from the work of Schoenberg on spherically symmetric distributions.
Journal ArticleDOI
Isotropy and Sphericity: Some Characterisations of the Normal Distribution
TL;DR: In this article, it was shown that the Euclidean random variables are normal if n = 2 and n = 3, and the case of Hilbert spaces is studied in the case n = 4.
Journal ArticleDOI
On the laws of cauchy and gauss
TL;DR: In this article, the authors derived some interesting general properties possessed by the class of distribution laws and deduced a characterization of the normal distribution under some conditions on the distribution function $F(x)$.