The probability that two samples in the plane will have disjoint convex hulls-Reference-Cited by-同舟云学术

The probability that two samples in the plane will have disjoint convex hulls

Published:1978-12 Issue:4 Volume:15 Page:790-802
ISSN:0021-9002
Container-title:Journal of Applied Probability
language:en
Short-container-title:Journal of Applied Probability

Author:

Rogers L. C. G.

Abstract

Suppose given an absolutely continuous distribution on the plane, and points Pi, · · ·, Pj, Πt, · · ·, Πk chosen independently according to the given distribution. Denoting by Gj the convex hull of {Pi, · · ·, Pj}, and by Γk the convex hull of (Πt, · · ·, Πk}, and writing pjk for the probability that Gj and Γk are disjoint, certain properties of the array {pjk; j, k = 1,2, · · ·} are established, including a recurrence generating the array in terms of {p1n; n = 1,2, · · ·}, and asymptotic results for {pnn; n = 1,2, · · ·}. Some examples are considered.

Publisher

Cambridge University Press (CUP)

Subject

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

Reference5 articles.

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2. �ber die konvexe H�lle von n zuf�llig gew�hlten Punkten

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