A symptotic Behavior of Convolution of Dependent Random Variables with Heavy-Tailed Distributions

被引：0
|
作者：
Ranjbar, V. Y. [1 ]
Amini, M. [1 ]
Bozorgnia, A. [1 ]
机构：
[1] Ferdowsi Univ Mashhad, Fac Math Sci, Ordered & Spatial Data Ctr Excellence, Dept Stat, Mashhad 917551159, Iran
来源：
THAI JOURNAL OF MATHEMATICS | 2009年 / 7卷 / 02期
关键词：
Weakly Negative Dependence (WND); Negative Quadratic Dependent (NQD); Heavy-Tailed; Long-Tailed; Asymptotic behavior;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the asymptotic behavior of the tail of X-1 + X-2 in a dependent framework; where X-1 and X-2 are two positive heavy-tailed random variables with continuous joint and common marginal distribution functions F (x, y) and F (x), respectively; and for some classes of heavy-tailed distributions, we obtain some bounds and convolution properties. Furthermore, we prove P (vertical bar X-1 - X-2 vertical bar > x) similar to a.P (vertical bar X vertical bar > x) as x -> infinity, where a is a constant and X-1, X-2 are dependent random variables.
引用
收藏
页码：217 / 230
页数：14
相关论文
共 50 条
  • [1] Asymptotic Behavior of Convolution of Dependent Random Variables with Heavy-Tailed Distributions
    Ranjbar, Vahid Y.
    Amini, Mohammad
    Bozorgnia, Abolghasem
    [J]. THAI JOURNAL OF MATHEMATICS, 2009, 7 (01): : 21 - 34
  • [2] Tail behavior of the sums of dependent and heavy-tailed random variables
    Yu, Changjun
    Wang, Yuebao
    Cheng, Dongya
    [J]. JOURNAL OF THE KOREAN STATISTICAL SOCIETY, 2015, 44 (01) : 12 - 27
  • [3] Tail behavior of the sums of dependent and heavy-tailed random variables
    Changjun Yu
    Yuebao Wang
    Dongya Cheng
    [J]. Journal of the Korean Statistical Society, 2015, 44 : 12 - 27
  • [4] Asymptotic behavior of product of two heavy-tailed dependent random variables
    Vahid Ranjbar
    Mohammad Amini
    Jaap Geluk
    Abolghasem Bozorgnia
    [J]. Acta Mathematica Sinica, English Series, 2013, 29 : 355 - 364
  • [5] Asymptotic Behavior of Product of Two Heavy-tailed Dependent Random Variables
    Vahid RANJBAR
    Mohammad AMINI
    Jaap GELUK
    Abolghasem BOZORGNIA
    [J]. Acta Mathematica Sinica, 2013, 29 (02) - 364
  • [6] Asymptotic Behavior of Product of Two Heavy-tailed Dependent Random Variables
    Vahid RANJBAR
    Mohammad AMINI
    Jaap GELUK
    Abolghasem BOZORGNIA
    [J]. Acta Mathematica Sinica,English Series, 2013, (02) : 355 - 364
  • [7] Asymptotic behavior of product of two heavy-tailed dependent random variables
    Ranjbar, Vahid
    Amini, Mohammad
    Geluk, Jaap
    Bozorgnia, Abolghasem
    [J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2013, 29 (02) : 355 - 364
  • [8] The asymptotic behavior of quadratic forms in heavy-tailed strongly dependent random variables
    Kokoszka, PS
    Taqqu, MS
    [J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1997, 66 (01) : 21 - 40
  • [9] The asymptotic behavior of quadratic forms in heavy-tailed strongly dependent random variables
    Kokoszka, P. S.
    Taqqu, M. S.
    [J]. Stochastic Processes and their Applications, 66 (01):
  • [10] Minimum of heavy-tailed random variables is not heavy tailed
    Leipus, Remigijus
    Siaulys, Jonas
    Konstantinides, Dimitrios
    [J]. AIMS MATHEMATICS, 2023, 8 (06): : 13066 - 13072
12345