重尾子族与随机和精确大偏差的几个结论

重尾子族与随机和精确大偏差的几个结论

王金亮, 周明法, 王侃民

九江学院理学院，江西省九江332005

收稿日期:2004-12-13 修回日期:1900-01-01 出版日期:2005-09-26 发布日期:2005-09-26
通讯作者: 王金亮

Some Conclusions about Heavy-tailed Subclasses and Refined Large Deviations

WANG Jin-liang，ZHOU Ming-fa，WANG Kan-min

Department of Science，Jiujiang University，Jiujiang 332005，Jiangxi Province，China

Received:2004-12-13 Revised:1900-01-01 Online:2005-09-26 Published:2005-09-26
Contact: WANG Jin-liang

摘要/Abstract

摘要： 探讨了经典的两个重尾随机变量族ERV族和D族的关系，发现D族主要是由ERV族构成的，得到了D族上随机和精确大偏差结论；另外，对于尾分布重于λ·e^-c的情况，也得到了类似的结论.

关键词: 重尾随机变量, 精确大偏差, 矩母函数, 次指数分布

Abstract: We have discovered the relationship between classical heavy-tailed class D of random variables and heavy-tailed class ERV which can be more easily dealt with，and we have obtained the accurate large deviation conclusion about random sums of heavy-tailed random variables that belongs to the class D. As to the random sums when summands’distribution functions are heavier than λ·e^-c, we have got similar conclusions.

Key words: heavy-tailed random variable, accurate large deviation, moment generating function, subexponential distribution

中图分类号:

O211.1

王金亮, 周明法, 王侃民. 重尾子族与随机和精确大偏差的几个结论[J]. J4, 2005, 43(05): 567-572.

WANG Jin-liang，ZHOU Ming-fa，WANG Kan-min. Some Conclusions about Heavy-tailed Subclasses and Refined Large Deviations[J]. J4, 2005, 43(05): 567-572.