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A class of spherical and elliptical distributions with Gaussian-like limit properties

Sherlock, Christopher and Elton, Daniel (2012) A class of spherical and elliptical distributions with Gaussian-like limit properties. Interational Journal of Statistics and Probability, 2012. ISSN 1927-7032

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Abstract

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.

Item Type: Article
Journal or Publication Title: Interational Journal of Statistics and Probability
Uncontrolled Keywords: Gaussian limit
Subjects:
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 53588
Deposited By: ep_importer_pure
Deposited On: 19 Apr 2012 15:03
Refereed?: Yes
Published?: Published
Last Modified: 07 Jan 2015 17:19
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/53588

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