THE NUMBER OF EXTREME-POINTS IN THE CONVEX-HULL OF A RANDOM SAMPLE

被引：32

作者：

ALDOUS, DJ

FRISTEDT, B

GRIFFIN, PS

PRUITT, WE

机构：

[1] UNIV MINNESOTA,SCH MATH,MINNEAPOLIS,MN 55455

[2] SYRACUSE UNIV,DEPT MATH,SYRACUSE,NY 13210

来源：

JOURNAL OF APPLIED PROBABILITY | 1991年 / 28卷 / 02期

关键词：

LIMIT DISTRIBUTION; MEAN; VARIANCE;

D O I：

10.2307/3214867

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：

Let {X(k)} 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(l),..., X(n)} is shown to have a limiting distribution which is obtained explicitly. Precise information about the mean and variance of the limit distribution is obtained.

引用

页码：287 / 304

页数：18

共 10 条

[1] ON LIMITING LAWS FOR THE CONVEX-HULL OF A SAMPLE [J].

BROZIUS, H ;

DEHAAN, L .

JOURNAL OF APPLIED PROBABILITY, 1987, 24 (04) :852-862

[2] CONVEX HULLS OF POINTS DISTRIBUTED BY ROTATIONAL SYMMETRY [J].

CARNAL, H .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1970, 15 (02) :168-&

[3]

DAVIS R, 1987, COMM STAT STOCHASTIC, V3, P1

[4] THE CONVEX-HULL OF A SPHERICALLY SYMMETRIC SAMPLE [J].

EDDY, WF ;

GALE, JD .

ADVANCES IN APPLIED PROBABILITY, 1981, 13 (04) :751-763

[5]

EFRON B, 1965, BIOMETRIKA, V52, P331, DOI 10.2307/2333687

[6] LIMIT-THEOREMS FOR CONVEX HULLS [J].

GROENEBOOM, P .

PROBABILITY THEORY AND RELATED FIELDS, 1988, 79 (03) :327-368

[7] COVERAGE PROBLEMS AND RANDOM CONVEX HULLS [J].

JEWELL, NP ;

ROMANO, JP .

JOURNAL OF APPLIED PROBABILITY, 1982, 19 (03) :546-561

[8]

MALLER RA, 1984, P LOND MATH SOC, V49, P385

[9]

Renyi A., 1963, Z WAHRSCHEINLICHKEIT, V2, P75, DOI DOI 10.1007/BF00535300

[10]

Wendel JG., 1963, MATH SCAND, V11, P109

← 1 →