COMPOUND POISSON APPROXIMATION FOR NONNEGATIVE RANDOM-VARIABLES VIA STEIN METHOD

被引：104

作者：

BARBOUR, AD

CHEN, LHY

LOH, WL

机构：

[1] NATL UNIV SINGAPORE, DEPT MATH, SINGAPORE 0511, SINGAPORE

[2] PURDUE UNIV, DEPT STAT, W LAFAYETTE, IN 47907 USA

来源：

ANNALS OF PROBABILITY | 1992年 / 20卷 / 04期

关键词：

STEINS METHOD; COMPOUND POISSON DISTRIBUTION; TOTAL VARIATION DISTANCE; RATE OF CONVERGENCE;

D O I：

10.1214/aop/1176989531

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 aim of this paper is to extend Stein's method to a compound Poisson distribution setting. The compound Poisson distributions of concern here are those of the form POIS(v), where v is a finite positive measure on (0, infinity). A number of results related to these distributions are established. These in turn are used in a number of examples to give bounds for the error in the compound Poisson approximation to the distribution of a sum of random variables.

引用

页码：1843 / 1866

页数：24

共 31 条

[1]

Aldous D., 1989, APPL MATH SCI, V77

[2] 2 MOMENTS SUFFICE FOR POISSON APPROXIMATIONS - THE CHEN-STEIN METHOD [J].