TY - JOUR

T1 - A class of spherical and elliptical distributions with Gaussian-like limit properties

AU - Sherlock, Christopher

AU - Elton, Daniel

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Gaussian limit

U2 - 10.1155/2012/467187

DO - 10.1155/2012/467187

M3 - Journal article

VL - 2012

JO - International Journal of Statistics and Probability

JF - International Journal of Statistics and Probability

SN - 1927-7032

M1 - 467187

ER -