Exchangeable pairs and Poisson approximation

Details Exchangeable pairs and Poisson approximation Exchangeable pairs and Poisson approximation

2004-11-23

arxiv.org/abs/math/0411525v3

Probability Surveys 2005, Vol. 2, 64-106

Mathematics

Probability

Published at http://dx.doi.org/10.1214/154957805100000096 in the Probability Surveys (http://www.i-journals.org/ps/) by the In

Scientific paper

10.1214/154957805100000096

This is a survey paper on Poisson approximation using Stein's method of exchangeable pairs. We illustrate using Poisson-binomial trials and many variations on three classical problems of combinatorial probability: the matching problem, the coupon collector's problem, and the birthday problem. While many details are new, the results are closely related to a body of work developed by Andrew Barbour, Louis Chen, Richard Arratia, Lou Gordon, Larry Goldstein, and their collaborators. Some comparison with these other approaches is offered.

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