A Class of Spherical and Elliptical Distributions with Gaussian-Like Limit Properties
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2012/467187 |
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| Summary: | 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. |
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| ISSN: | 1687-952X 1687-9538 |