Lower limits and upper limits for tails of random sums supported on R

被引：13

作者：

Yu, Changjun ^{[1
]}

Wang, Yuebao ^{[1
]}

Cui, Zhaolei ^{[1
]}

机构：

[1] Soochow Univ, Dept Math, Suzhou 215006, Peoples R China

来源：

STATISTICS & PROBABILITY LETTERS | 2010年 / 80卷 / 13-14期

基金：

美国国家科学基金会;

关键词：

Lower limits; Upper limits; Random sums; Local distribution; Density; CONVOLUTION EQUIVALENCE; ASYMPTOTICS;

D O I：

10.1016/j.spl.2010.03.005

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Based on Rudin (1973), Foss and Korshunov (2007) and Denisov et al. (2008), we study the lower limits and upper limits of the quotients of tails (F*(tau)) over bar (x)/(F) over bar (x) as x ->infinity, where tau is a non-negative integer-valued random variable and F is a distribution supported on R. Some of the new results, which are different from the corresponding results of R+, give a positive answer to Problem 2 of Watanabe (2008) under certain conditions. In addition, we give some corresponding results for the local versions and density versions. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：1111 / 1120

页数：10

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