Compound Poisson approximation: A user's guide

• 成果类型: Article
• 署名作者: Barbour, AD; Chryssaphinou, O
• 署名单位: University of Zurich; National & Kapodistrian University of Athens
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2001
• 页码: 964-1002
• 关键词: of-n-f; consecutive-k; random-variables; sequence; reliability; moments; systems; patterns; number

摘要

Compound Poisson approximation is a useful tool in a variety of applications, including insurance mathematics, reliability theory, and molecular sequence analysis. In this paper, we review the ways in which Stein's method can currently be used to derive bounds on the error in such approximations. The theoretical basis for the construction of error bounds is systematically discussed, and a number of specific examples are used for illustration. We give no numerical comparisons in this paper, contenting ourselves with references to the literature, where compound Poisson approximations derived using Stein's method are shown frequently to improve upon bounds obtained from problem specific, ad hoc methods.