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

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.

Type
Research Papers
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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