Asymptotics of random sums of negatively dependent random variables in the presence of dominatedly varying tails

被引：5

作者：

Yang, Yang ^{[1
,2
]}

Leipus, Remigijus ^{[3
,4
]}

Siaulys, Jonas ^{[3
]}

机构：

[1] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China

[2] Nanjing Audit Univ, Sch Math & Stat, Nanjing 210029, Jiangsu, Peoples R China

[3] Vilnius Univ, Fac Math & Informat, LT-03225 Vilnius, Lithuania

[4] Vilnius Univ, Inst Math & Informat, LT-08663 Vilnius, Lithuania

来源：

LITHUANIAN MATHEMATICAL JOURNAL | 2012年 / 52卷 / 02期

基金：

美国国家科学基金会; 中国博士后科学基金;

关键词：

negative dependence; dominated variation; random sums; dependent compound renewal risk model; PRECISE LARGE DEVIATIONS; HEAVY TAILS; DISTRIBUTIONS; BEHAVIOR;

D O I：

10.1007/s10986-012-9169-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (1) (2) be a sequence of negatively dependent and identically distributed random variables, and let be a counting random variable independent of 's. In this paper, we study the asymptotics for the tail probability of the random sum S-N = Sigma(N)(k=1) in the presence of heavy tails. We consider the following three cases: (i) () = (( (1) )), and the distribution function (d.f.) of (1) is dominatedly varying; (ii) ( (1) ) = (()), and the d.f. of is dominatedly varying; (iii) the tails of (1) and are asymptotically comparable and dominatedly varying.

引用

页码：222 / 232

页数：11

共 50 条

[21] Moderate deviations for the random weighted sums of WUOD random variables with consistently varying tails
Lu, Dawei
Chen, Xiaoyan
Feng, Jinghai
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2020, 49 (03) : 531 - 551
[22] Moderate deviations for the random weighted sums of END random variables with consistently varying tails
Dong, Yinghua
Wang, Dingcheng
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2017, 46 (20) : 10116 - 10134
[23] CLOSURE PROPERTY AND TAIL PROBABILITY ASYMPTOTICS FOR RANDOMLY WEIGHTED SUMS OF DEPENDENT RANDOM VARIABLES WITH HEAVY TAILS
Dindiene, Lina
Leipus, Remigijus
Siaulys, Jonas
[J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2017, 54 (06) : 1879 - 1903
[24] Precise large deviations for sums of random variables with consistently varying tails
Ng, KW
Tang, QH
Yan, JA
Yang, HL
[J]. JOURNAL OF APPLIED PROBABILITY, 2004, 41 (01) : 93 - 107
[25] Complete convergence for weighted sums of negatively dependent random variables
Sung, Soo Hak
[J]. STATISTICAL PAPERS, 2012, 53 (01) : 73 - 82
[26] Complete convergence for weighted sums of negatively dependent random variables
Soo Hak Sung
[J]. Statistical Papers, 2012, 53 : 73 - 82
[27] Some Inequalities of Partial Sums for Negatively Dependent Random Variables
Huang, Haiwu
Wu, Qunying
Deng, Guangming
[J]. MECHANICAL ENGINEERING AND INTELLIGENT SYSTEMS, PTS 1 AND 2, 2012, 195-196 : 694 - +
[28] Precise Large Deviations for Sums of Independent Random Variables with Consistently Varying Tails
Lu, Dawei
Song, Lixin
Xu, Ying
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2014, 43 (01) : 28 - 43
[29] Precise large deviations for negatively associated random variables with consistently varying tails
Liu, Yan
[J]. STATISTICS & PROBABILITY LETTERS, 2007, 77 (02) : 181 - 189
[30] Asymptotics for dependent sums of random vectors
Cooper, C
[J]. RANDOM STRUCTURES & ALGORITHMS, 1999, 14 (03) : 267 - 292

← 1 2 3 4 5 →