Approximation of partial sums of arbitrary iid random variables and the precision of the usual exponential upper bound

• 成果类型: Article
• 署名作者: Hahn, MG; Klass, MJ
• 署名单位: Tufts University; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1997
• 页码: 1451-1470
• 关键词: independent random-variables; large deviations

摘要

This paper quantifies the degree to which exponential bounds can be used to approximate tail probabilities of partial sums of arbitrary lid. random variables. The introduction of a single truncation allows the usual exponential upper bound to apply usefully whenever the summands are arbitrary lid. random variables. More specifically, let n be a fixed natural number and let Z, Z(1), Z(2),..., Z(n) be arbitrary i.i.d. random variables We construct a function F-Z,F- n(a), derived from the probability bf occurrence of one or more large summands plus an upper bound of exponential type such that for some constant C* > 0 (independent of Z, n and a) and all real a, [GRAPHICS] Furthermore, examples show that the upper and lower bounds are achievable.