On Stein’s factors for Poisson approximation in Wasserstein distance

Bernoulli

Volumn 12, Issue 6, 2006, Pages 943-954

  Barbour, A D ^a   Xia, Aihua ^b  

^a UNIVERSITY OF ZURICH   (Switzerland)

^b UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Poisson approximation; Stein factors; Stein s method; Wasserstein distance

Indexed keywords

EID: 42449083329     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/bj/1165269145     Document Type: Article

References (9)

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2. Barbour, A.D. and Eagleson, G.K. (1987) An improved Poisson limit theorem for sums of dissociated random variables. J Appl. Probab., 24, 586-599.
3. Barbour, A.D. and Hall, P. (1984) On the rate of Poisson convergence. Math. Proc. Cambridge Philos. Soc., 95, 473-480.
4. Barbour, A.D., Holst, L. and Janson, S. (1992) Poisson Approximation. Oxford: Oxford University Press.
5. Brown, T.C. and Xia, A. (2001) Stein’s method and birth-death processes. Ann. Probab., 29, 1373-1403.
6. Cekanavicius, V. and Vaitkus, P. (2001) Centered Poisson approximation by the Stein method. Lithuanian Math. J., 41, 319-329.
7. Chen, L.H.Y. (1975) Poisson approximation for dependent trials. Ann. Probab., 3, 534-545.
8. Rollin, A. (2005) Approximation of sums of conditionally independent variables by the translated Poisson distribution. Bernoulli, 11, 1115-1128.
9. Stein, C. (1972) A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. In Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 2, pp. 583-602. Berkeley: University of California Press