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
收藏
页码：1111 / 1120
页数：10
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