| A sharp inequality for the tail probabilities of sums of i.i.d. r.v.’s with dominatedly varying tails |
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| 引用本文： | 唐启鹤,严加安.A sharp inequality for the tail probabilities of sums of i.i.d. r.v.’s with dominatedly varying tails[J].中国科学A辑(英文版),2002,45(8):1006-1011. |
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| 作者姓名： | 唐启鹤 严加安 |
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| 作者单位： | 唐启鹤(Department of Quantitative Economics, University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands);严加安(Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China) |
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| 基金项目： | 国家重点基础研究发展计划(973计划),中国科学院知识创新工程项目 |
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| 摘 要： | Let F be a distribution function supported on (-∞, ∞) with a finite mean μ. In this note weshow that if its tail F = 1 - F is dominatedly varying, then for any γ＞ max{μ, 0}, there exist C(γ) ＞ 0 and D(γ) ＞ 0 such thatC(γ)nF(x) ≤ Fn*(x) ≤ D(γ)nF(x),for all n ≥ 1 and all x ≥γn. This inequality sharpens a classical inequality for the subexponential distributioncase.
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