ON THE ASYMPTOTIC DISTRIBUTION OF THE AREA OUTSIDE A RANDOM CONVEX HULL IN A DISK

被引：31

作者：

Hsing, Tailen ^{[1
]}

机构：

[1] Texas A&M Univ, Dept Stat, College Stn, TX 77843 USA

来源：

ANNALS OF APPLIED PROBABILITY | 1994年 / 4卷 / 02期

关键词：

Asymptotic distribution; convex hull; point processes;

D O I：

10.1214/aoap/1177005069

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The asymptotic distribution of the area V-n outside the convex hull of n i.i.d. points uniformly distributed on the two-dimensional unit disk is studied. The asymptotic variance of V-n is found to be of the order n(-5/3), and the asymptotic distribution of V-n shown to be normal. The results are obtained by carefully analyzing the strength of dependence between sample points at different locations close to the boundary of the unit disk.

引用

页码：478 / 493

页数：16