Tail behavior of negatively associated heavy-tailed sums

Journal of Applied Probability

Volumn 43, Issue 2, 2006, Pages 587-593

  Geluk, Jaap ^a   Ng, Kai W ^b  

^a KHALIFA UNIVERSITY   (United Arab Emirates)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Asymptotics; Negative association; Partial sum; Subexponentiality; Tail probability

Indexed keywords

EID: 33845292215     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1152413743     Document Type: Article

References (23)

1. ALAM, K. AND SAXENA, K. M. L. (1981). Positive dependence in multivariate distributions. Commun. Statist. A 10, 1183-1196.
2. ASMUSSEN, S. (2000). Ruin Probabilities (Adv. Ser. Statist. Sci. Appl. Prob. 2). World Scientific, River Edge, NJ.
3. ASMUSSEN, S., KROESE, D. P. AND RUBINSTEIN, R. Y. (2005). Heavy tails, importance sampling and cross-entropy. Stoch. Models 21, 57-76.
4. BINGHAM, N. H., GOLDIE, C. M. AND TEUGELS, J. L. (1987). Regular Variation (Encyclopedia Math. Appl. 27). Cambridge University Press.
5. BOXMA, O. J., FOSS, S. G., LASGOUTTES, J.-M. AND NÚÑEZ QUEIJA, R. (2004). Waiting time asymptotics in the single server queue with service in random order. Queueing Systems 46, 35-73.
6. EMBRECHTS, P. AND GOLDIE, C. M. (1980). On closure and factorization properties of subexponential and related distributions. J. Austral. Math. Soc. Ser. A 29, 243-256.
7. EMBRECHTS, P., GOLDIE, C. M. AND VERAVERBEKE, N. (1979). Subexponentiality and infinite divisibility. Z. Wahrscheinlichkeitsth. 49, 335-347.
8. EMBRECHTS, P., KLÜPPELBERG, C. AND MIKOSCH, T. (1997). Modelling Extremal Events (Appl. Math. (New York) 33). Springer, Berlin.
9. FELLER, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. 2, 2nd edn. John Wiley, New York.
10. GELUK, J. (2004). Asymptotics in the symmetrization inequality. Statist. Prob. Lett. 69, 63-68.
11. GELUK, J. L. AND DE VRIES, C. G. (2006). Weighted sums of subexponential random variables and asymptotic dependence between returns on reinsurance equities. Insurance Math. Econom. 38, 39-56.
12. JOAG-DEV, K. AND PROSCHAN, F. (1983). Negative association of random variables, with applications. Ann. Statist. 11, 286-295.
13. NG, K. W. AND TANG, Q. (2004). Asymptotic behavior of tail and local probabilities for sums of subexponential random variables. J. Appl. Prob. 41, 108-116.
14. NG, K. W., TANG, Q. H. AND YANG, H. (2002). Maxima of sums of heavy-tailed random variables. ASTIN Bull. 32, 43-55.
15. PAKES, A. G. (2004). Convolution equivalence and infinite divisibility. J. Appl. Prob. 41, 407-424.
16. PENG, L. AND YAO, Q. (2004). Nonparametric regression under dependent errors with infinite variance. Ann. Inst. Statist. Math. 56, 73-86.
17. PETROV, V. V. (1975). A generalization of an inequality of Levy. Theory Prob. Appl. 20, 141-145.
18. ROLSKI, T., SCHMIDLI, H., SCHMIDT, V. AND TEUGELS, J. (1999). Stochastic Processes for Insurance and Finance. John Wiley, Chichester.
19. SGIBNEV, M. S. (1996). On the distribution of the maxima of partial sums. Statist. Prob. Lett. 28, 235-238.
20. TANG, Q. AND YAN, J. (2002). A sharp inequality for the tail probabilities of sums of i.i.d. r.v.'s with dominatedly varying tails. Sci. China Ser. A 45, 1006-1011.
21. WANG, D. AND TANG, Q. (2004). Maxima of sums and random sums for negatively associated random variables with heavy tails. Statist. Prob. Lett. 68, 287-295.
22. WILLEKENS, E. (1986). Hogere orde theorie voor subexponentiele verdelingen. Doctoral Thesis, University of Leuven.
23. ZWART, B., BORST, S. AND MANDIES, M. (2004). Exact asymptotics for fluid queues fed by multiple heavy-tailed on-off flows. Ann. Appl. Prob. 14, 903-957.