A Class of Spherical and Elliptical Distributions with Gaussian-Like Limit Properties
Joint Authors
Source
Journal of Probability and Statistics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-02-28
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
We present a class of spherically symmetric random variables defined by the property that as dimension increases to infinity the mass becomes concentrated in a hyperspherical shell, the width of which is negligible compared to its radius.
We provide a sufficient condition for this property in terms of the functional form of the density and then show that the property carries through to equivalent elliptically symmetric distributions, provided that the contours are not too eccentric, in a sense which we make precise.
Individual components of such distributions possess a number of appealing Gaussian-like limit properties, in particular that the limiting one-dimensional marginal distribution along any component is Gaussian.
American Psychological Association (APA)
Sherlock, Chris& Elton, Daniel. 2012. A Class of Spherical and Elliptical Distributions with Gaussian-Like Limit Properties. Journal of Probability and Statistics،Vol. 2012, no. 2012, pp.1-17.
https://search.emarefa.net/detail/BIM-473798
Modern Language Association (MLA)
Sherlock, Chris& Elton, Daniel. A Class of Spherical and Elliptical Distributions with Gaussian-Like Limit Properties. Journal of Probability and Statistics No. 2012 (2012), pp.1-17.
https://search.emarefa.net/detail/BIM-473798
American Medical Association (AMA)
Sherlock, Chris& Elton, Daniel. A Class of Spherical and Elliptical Distributions with Gaussian-Like Limit Properties. Journal of Probability and Statistics. 2012. Vol. 2012, no. 2012, pp.1-17.
https://search.emarefa.net/detail/BIM-473798
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-473798