Exchangeable pairs and Poisson approximation
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.
Permanent link to this document: http://projecteuclid.org/euclid.ps/1109608868
Digital Object Identifier: doi:10.1214/154957805100000096
Mathematical Reviews number (MathSciNet): MR2121796
Zentralblatt MATH identifier: 1189.60072