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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| 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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| _version_ | 1832545824929742848 |
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| author | Chris Sherlock Daniel Elton |
| author_facet | Chris Sherlock Daniel Elton |
| author_sort | Chris Sherlock |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f6bb0a23e7c04594bd75ef624fe8fc97 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-f6bb0a23e7c04594bd75ef624fe8fc972025-02-03T07:24:41ZengWileyJournal of Probability and Statistics1687-952X1687-95382012-01-01201210.1155/2012/467187467187A Class of Spherical and Elliptical Distributions with Gaussian-Like Limit PropertiesChris Sherlock0Daniel Elton1Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UKDepartment of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UKWe 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.http://dx.doi.org/10.1155/2012/467187 |
| spellingShingle | Chris Sherlock Daniel Elton A Class of Spherical and Elliptical Distributions with Gaussian-Like Limit Properties Journal of Probability and Statistics |
| title | A Class of Spherical and Elliptical Distributions with
Gaussian-Like Limit Properties |
| title_full | A Class of Spherical and Elliptical Distributions with
Gaussian-Like Limit Properties |
| title_fullStr | A Class of Spherical and Elliptical Distributions with
Gaussian-Like Limit Properties |
| title_full_unstemmed | A Class of Spherical and Elliptical Distributions with
Gaussian-Like Limit Properties |
| title_short | A Class of Spherical and Elliptical Distributions with
Gaussian-Like Limit Properties |
| title_sort | class of spherical and elliptical distributions with gaussian like limit properties |
| url | http://dx.doi.org/10.1155/2012/467187 |
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