The number of extreme points in the convex hull of a random sample
The number of extreme points in the convex hull of a random sample
复制标题
随机样本凸包中极值点的数量
DOI：
--
复制
发表时间：
1991
影响因子：
1
通讯作者：
W. Pruitt
中科院分区：
文献类型：
--
作者：
D. Aldous;B. Fristedt;P. Griffin;W. Pruitt
设{Xk }为i. i. d。序列取λ 2中的值，其中径向分量和球面分量独立，并且径向分量具有缓慢变化的尾部的分布。证明了{X1，· ··，Xn }的凸船体中极值点的个数具有一个极限分布，并给出了该极限分布的显式表达式.得到了极限分布的均值和方差的精确信息。
Let {Xk } be an i.i.d. sequence taking values in ℝ2 with 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 {X 1, · ··, 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.