Compound Poisson Approximation for Dissociated Random Variables via Stein's Method

Combinatorics Probability and Computing

Volumn 8, Issue 4, 1999, Pages 335-346

  Eichelsbacher, Peter ^a   Roos, MaŁgorzata ^b  

^a BIELEFELD UNIVERSITY   (Germany)

^b UNIVERSITY OF ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033432266     PISSN: 09635483     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0963548399003880     Document Type: Article

References (12)

1. Aldous, D. J. (1989) Probability Approximations via the Poisson Clumping Heuristic, Springer, New York.
2. Arratia, R., Goldstein, L. and Gordon, L. (1990) Poisson approximation and the Chen-Stein method. Statist. Science 5 403-434.
3. Barbour, A. D., Chen, L. H. and Loh, W.-L. (1992) Compound Poisson approximation for nonnegative random variables via Stein's method. Ann. Probab. 20 1843-1866.
4. Barbour, A. D., Chryssaphinou, O. and Roos, M. (1996) Compound Poisson approximation in systems reliability. Naval Research Logistics 43 251-264.
5. Barbour A. D. and Eagleson, G. K. (1984) Poisson convergence for dissociated statistics. J. Royal Statist. Soc. B 46 397-402.
6. Barbour, A. D., Holst, L. and Janson, S. (1992) Poisson Approximation, Oxford University Press, Oxford.
7. Barbour, A. D. and Utev, S. (1999) Compound Poisson approximation in total variation. Stoch. Process. Appl. 82 89-125.
8. Barbour, A. D. and Utev, S. (1998) Solving the Stein equation in compound Poisson approximation. Adv. Appl. Probab. 30 449-475.
9. Lee, A. J. (1990) U-Statistics: Theory and Practice, Marcel Dekker, New York.
10. Roos, M. (1993) Stein-Chen method for compound Poisson approximation. PhD thesis, University of Zürich, Switzerland.
11. Roos, M. (1994) Stein-Chen method for compound Poisson approximation: the coupling approach. Probab. Theory Math. Statist. 4 645-660.
12. Roos, M. (1994) Stein's method for compound Poisson approximation: the local approach. Ann. Appl. Probab. 4 1177-1187.