Exchangeable pairs and Poisson approximation. (English) Zbl 1189.60072
Summary: 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.
MSC:
60F99 | Limit theorems in probability theory |
60C05 | Combinatorial probability |
60-02 | Research exposition (monographs, survey articles) pertaining to probability theory |