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The number of extreme points in the convex hull of a random sample

Published online by Cambridge University Press:  14 July 2016

David J. Aldous ,
Bert Fristedt ,
Philip S. Griffin  and
William E. Pruitt
David J. Aldous*
Affiliation:
University of California
Bert Fristedt*
Affiliation:
University of Minnesota
Philip S. Griffin*
Affiliation:
Syracuse University
William E. Pruitt*
Affiliation:
University of Minnesota
*
∗Postal address: Department of Statistics, University of California, 367 Evans Hall, Berkeley, CA 94720, USA.
∗∗Postal address: School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church Street S. E., Minneapolis, MN 55455, USA.
∗∗∗Postal address: Department of Mathematics, Syracuse University, 200 Carnegie, Syracuse, NY 13244–1150, USA.
∗∗Postal address: School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church Street S. E., Minneapolis, MN 55455, USA.
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Abstract

Let {Xk} be an i.i.d. sequence taking values in ℝ2 with the radial and spherical components independent and the radial component having a distribution with slowly varying tail. The number of extreme points in the convex hull of {X1, · ··, Xn} is shown to have a limiting distribution which is obtained explicitly. Precise information about the mean and variance of the limit distribution is obtained.

Keywords

LIMIT DISTRIBUTIONMEANVARIANCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 2 , June 1991 , pp. 287 - 304
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

Research partially supported by NSF Grant MCS 87–01426.

Research partially supported by NSF Grants DMS 87–01866 (BF) and DMS 86–03437 (WEP).

Research partially supported by NSF Grant DMS 87–00928.

References

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