LIMIT-THEOREMS FOR FUNCTIONALS OF CONVEX HULLS

被引:35
作者
CABO, AJ
GROENEBOOM, P
机构
[1] Mathematics Department, Delft University of Technology, Delft, 2628 CD
关键词
Mathematics Subject Classifications (1991): 52A22; 52A38; 60G44; 60G55;
D O I
10.1007/BF01204952
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
In [4] a central limit theorem for the number of vertices of the convex hull of a uniform sample from the interior of a convex polygon is derived. This is done by approximating the process of vertices of the convex hull by the process of extreme points of a Poisson point process and by considering the latter process of extreme points as a Markov process (for a particular parametrization). We show that this method can also be applied to derive limit theorems for the boundary length and for the area of the convex hull. This extends results of Renyi and Sulanke (1963) and Buchta (1984), and shows that the boundary length and the area have a strikingly different probabilistic behavior.
引用
收藏
页码:31 / 55
页数:25
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