The number of extreme points in the convex hull of a random sample

Abstract

Let {Xk} be an i.i.d. sequence taking values in ℝ2with the radial and spherical components independent and the radial component having a distribution with slowly varying tail. The number of extreme points in the convex hull of {X1, · ··,Xn} is shown to have a limiting distribution which is obtained explicitly. Precise information about the mean and variance of the limit distribution is obtained.