On the convex hull of n random points on a circle

Author:

Carnal H.,Hüsler J.

Abstract

We consider the convex hull of a sample of n randomly placed points in a unit circle. Obviously not all of the n points are needed to construct the convex hull. We show that asymptotically only the points belonging to a certain ring are used for the convex hull, where the size of the ring decreases at a certain rate such that the error of not completely correct construction of the convex hull by the particular subset of points tends to 0.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Reference9 articles.

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1. Asymptotics of the convex hull of spherically symmetric samples;Discrete Applied Mathematics;2011-02

2. Stochastic and Integral Geometry;Probability and Its Applications;2008

3. On the Hausdorff distance between a convex set and an interior random convex hull;Advances in Applied Probability;1998-06

4. On the Hausdorff distance between a convex set and an interior random convex hull;Advances in Applied Probability;1998-06

5. Stochastic Geometry;Handbook of Convex Geometry;1993

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