COMPOUND POISSON APPROXIMATION FOR NONNEGATIVE RANDOM-VARIABLES VIA STEIN METHOD

• 成果类型: Article
• 署名作者: BARBOUR, AD; CHEN, LHY; LOH, WL
• 署名单位: National University of Singapore; Purdue University System; Purdue University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989531
• 发表日期: 1992
• 页码: 1843-1866
• 关键词: limit-theorem; CONVERGENCE; distributions; expansions; sums

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.