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The distribution of the convex hull of a Gaussian sample

Published online by Cambridge University Press:  14 July 2016

William F. Eddy
William F. Eddy*
Affiliation:
Carnegie-Mellon University
*
∗Postal address: Department of Statistics, Carnegie-Mellon University, Schenley Park, Pittsburgh, PA 15213, U.S.A.
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Abstract

The distribution of the convex hull of a random sample of d-dimensional variables is described by embedding the collection of convex sets into the space of continuous functions on the unit sphere. Weak convergence of the normalized convex hull of a circular Gaussian sample to a process with extreme-value marginal distributions is demonstrated. The proof shows that an underlying sequence of point processes converges to a Poisson point process and then applies the continuous mapping theorem. Several properties of the limit process are determined.

Keywords

POISSON RANDOM MEASURECONTINUOUS FUNCTIONSEXTREME VALUE PROCESSWEAK CONVERGENCEPOINTWISE MAXIMUM
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 686 - 695
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

Research supported in part by NSF Grant MCS 78–02422 to Carnegie-Mellon University

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