Random convex hulls: a variance revisited
Steven Finch and Irene Hueter
Source: Adv. in Appl. Probab.
Volume 36, Number 4
(2004), 981-986.
Abstract
An exact expression is determined for the asymptotic constant
c2 in the limit theorem by P. Groeneboom (1988),
which states that the number of vertices of the convex hull of a
uniform sample of n random points from a circular disk
satisfies a central limit theorem, as n → ∞,
with asymptotic variance
2πc2n1/3.
Primary Subjects: 52A22
Secondary Subjects: 60D05
Keywords: Convex hull; random point set; random polygon; variance
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription.
Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aap/1103662954
Digital Object Identifier: doi:10.1239/aap/1103662954
Mathematical Reviews number (MathSciNet):
MR2119851
Zentralblatt MATH identifier:
02152505
References
Abramowitz, M. and Stegun, I. A. (1972). Handbook of Mathematical Functions, 9th printing. Dover, New York.
Buchta, C. (2002). An identity relating moments of functionals of convex hulls. Unpublished manuscript.
Efron, B. (1965). The convex hull of a random set of points. Biometrika 52, 331--343.
Mathematical Reviews (MathSciNet):
MR207004
Groeneboom, P. (1988). Limit theorems for convex hulls. Prob. Theory Relat. Fields 79, 327--368.
Mathematical Reviews (MathSciNet):
MR959514
Hsing, T. (1994). On the asymptotic distribution of the area outside a random convex hull in a disk. Ann. Appl. Prob. 4, 478--493.
Hueter, I. (1994). The convex hull of a normal sample. Adv. Appl. Prob. 26, 855--875.
Rényi, A. and Sulanke, R. (1963). Über die konvexe Hülle von $n$ zufällig gewählten Punkten. Z. Wahrscheinlichkeitsth. 2, 75--84.
Mathematical Reviews (MathSciNet):
MR156262
