A bound for the distribution of the sum of discrete associated or negatively associated random variables

• 成果类型: Article
• 署名作者: Boutsikas, MV; Koutras, MV
• 署名单位: University of Piraeus
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2000
• 页码: 1137-1150
• 关键词: compound poisson approximation

摘要

Let X-1, X-2,..., X-n be a sequence of integer-valued random variables that are either associated or negatively associated. We present a simple upper bound for the distance between the distribution of the sum of X-i and a sum of n independent random variables with the same marginals as X-i. An upper bound useful for establishing a compound Poisson approximation for Sigma X-n(i=1)i is also provided. The new bounds are of the same order as the much acclaimed Stein-Chen bound.