Uniform Estimates for Distributions of the Sum of i.i.d. Random Variables with Fat Tail in the Threshold Case

被引：0

作者：

Nakahara, Kenji

机构：

来源：

JOURNAL OF MATHEMATICAL SCIENCES-THE UNIVERSITY OF TOKYO | 2011年 / 18卷 / 04期

关键词：

INTEGRAL LIMIT THEOREMS; LARGE DEVIATIONS; CRAMERS CONDITION; ACCOUNT; HOLD;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show uniform estimates for distributions of the sum of i.i.d. random variables in the threshold case. Rozovskii showed several uniform estimates but the speed of convergence was not known. Our main uniform estimate implies a speed of convergence. We also compare our estimates with Nagaev's estimate which is valid in the non-threshold case and, moreover, give a necessary and sufficient condition for Nagaev's estimate to hold in the threshold case.

引用

页码：397 / 427

页数：31

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