Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-23T05:43:06.441Z Has data issue: false hasContentIssue false

On limiting laws for the convex hull of a sample

Published online by Cambridge University Press:  14 July 2016

Henk Brozius*
Affiliation:
Erasmus Universiteit Rotterdam
Laurens De Haan*
Affiliation:
Erasmus Universiteit Rotterdam
*
Postal address: Faculteit der Economische Wetenschappen, Erasmus Universiteit Rotterdam, Postbus 1738, 3000 DR Rotterdam, The Netherlands.
Postal address: Faculteit der Economische Wetenschappen, Erasmus Universiteit Rotterdam, Postbus 1738, 3000 DR Rotterdam, The Netherlands.

Abstract

The limiting behaviour of the convex hull of a sample in is studied using the support function. Results like that of Eddy and Gale (1981) are proved without the condition of spherical symmetry from that paper.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1987 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Billingsley, P. (1971) Weak convergence of measures: applications in probability. Society of Industrial and Applied Mathematics. Philadelphia.CrossRefGoogle Scholar
Eddy, W. F. (1980) The distribution of the convex hull of a Gaussian sample. J. Appl. Prob. 17, 686695.Google Scholar
Eddy, W. F. and Gale, J. D. (1981) The convex hull of a spherically symmetric sample. Adv. Appl. Prob. 13, 751763.Google Scholar
Gnedenko, B. V. (1943) Sur la distribution limite du terme maximum d'une série aléatoire. Ann. Math. 44, 423453.Google Scholar
De Haan, L. (1984) A spectral representation for max-stable processes. Ann. Prob. 12, 11941204.Google Scholar
De Haan, L. and Pickands, J. III (1986) Stationary min-stable stochastic processes. Prob. Theory Rel. Fields. 72, 477492.Google Scholar
De Haan, L. and Resnick, S. I. (1977) Limit theory for multivariate sample extremes. Z. Wahrscheinlichkeitsth. 40, 317337.CrossRefGoogle Scholar
Resnick, S. I. (1986) Point processes, regular variation and weak convergence. Adv. Appl. Prob. 18, 66138.Google Scholar
Rvaçeva, E. L. (1962) On the domains of attraction of multidimensional distributions. Select. Transl. Math. Statist. Prob. 2, 183207.Google Scholar
Valentine, F. A. (1964) Convex Sets. McGraw-Hill, New York.Google Scholar