The convex hull of a random set of points

Abstract

Various expectations concerning the convex hull of N independently and identically distributed random points in the plane or in space are evaluated. Integral expressions are given for the expected area, expected perimeter, expected probability content and expected number of sides. These integrals are shown to be particularly simple when the underlying distribution is normal or uniform over a disk or sphere.

Identifiers

DOI

10.1093/biomet/52.3-4.331

Citations and references