Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-15T11:08:17.802Z Has data issue: false hasContentIssue false
  • English
  • Français

Sums of Dependent Nonnegative Random Variables with Subexponential Tails

Part of:Distribution theoryMultivariate analysisStochastic processes

Published online by Cambridge University Press:  14 July 2016

Bangwon Ko and
Qihe Tang
Bangwon Ko*
Affiliation:
The University of Iowa
Qihe Tang*
Affiliation:
The University of Iowa
*
∗ Postal address: Department of Statistics and Actuarial Science, The University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA.
∗ Postal address: Department of Statistics and Actuarial Science, The University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

In this paper we study the asymptotic tail probabilities of sums of subexponential, nonnegative random variables, which are dependent according to certain general structures with tail independence. The results show that the subexponentiality of the summands eliminates the impact of the dependence on the tail behavior of the sums.

Keywords

Asymptoticscopuladependencesubexponentialityuniformity

MSC classification

Secondary:62E20: Asymptotic distribution theory60G70: Extreme value theory; extremal processes62H20: Measures of association (correlation, canonical correlation, etc.)

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 1 , March 2008, pp. 85 - 94
Copyright
Copyright © Applied Probability Trust 2008 

References

Albrecher, H., Asmussen, S. and Kortschak, D. (2006). Tail asymptotics for the sum of two heavy-tailed dependent risks. Extremes 9, 107–130.Google Scholar
Alink, S., Löwe, M. and Wüthrich, M. V. (2004). Diversification of aggregate dependent risks. Insurance Math. Econom. 35, 77–95.Google Scholar
Barbe, P., Fougères, A.-L. and Genest, C. (2006). On the tail behavior of sums of dependent risks. Astin Bull. 36, 361–373.CrossRefGoogle Scholar
Cai, J. and Tang, Q. (2004). On max-sum equivalence and convolution closure of heavy-tailed distributions and their applications. J. Appl. Prob. 41, 117–130.Google Scholar
Cline, D. B. H. (1986). Convolution tails, product tails and domains of attraction. Prob. Theory Relat. Fields 72, 529–557.CrossRefGoogle Scholar
Coles, S., Heffernan, J. and Tawn, J. (1999). Dependence measures for extreme value analyses. Extremes 2, 339–447.Google Scholar
Embrechts, P., Klüppelberg, C. and Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance. Springer, Berlin.CrossRefGoogle Scholar
Geluk, J. and Ng, K. (2006). Tail behavior of negatively associated heavy-tailed sums. J. Appl. Prob. 43, 587–593.CrossRefGoogle Scholar
Kortschak, D. and Albrecher, H. (2008). Asymptotic results for the sum of dependent nonidentically distributed random variables. To appear in Methodology Comput. Appl. Prob. Google Scholar
Lehmann, E. L. (1966). Some concepts of dependence. Ann. Math. Statist. 37, 1137–1153.Google Scholar
Nelsen, R. B. (2006). An Introduction to Copulas, 2nd edn. Springer, New York.Google Scholar
Tang, Q. (2008). Insensitivity to negative dependence of asymptotic tail probabilities of sums and maxima of sums. To appear in Stoch. Anal. Appl. Google Scholar
Tang, Q. and Tsitsiashvili, G. (2003). Randomly weighted sums of subexponential random variables with application to ruin theory. Extremes 6, 171–188.CrossRefGoogle Scholar