Sherlock, Christopher and Elton, Daniel (2012) A class of spherical and elliptical distributions with Gaussian-like limit properties. International Journal of Statistics and Probability, 2012. ISSN 1927-7032Full text not available from this repository.
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.
|Journal or Publication Title:||International Journal of Statistics and Probability|
|Uncontrolled Keywords:||Gaussian limit|
|Departments:||Faculty of Science and Technology > Mathematics and Statistics|
|Deposited On:||19 Apr 2012 15:03|
|Last Modified:||13 Jan 2016 14:09|
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