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Exchangeable pairs and Poisson approximation
release_tjrypmqgfjezpgm2nzo5ksr2ou
by
Sourav Chatterjee, Persi Diaconis, Elizabeth Meckes
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2005
Abstract
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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