Some applications of the Stein-Chen method for proving Poisson convergence
- 1 March 1989
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 21 (1) , 74-90
- https://doi.org/10.2307/1427198
Abstract
LetWbe a sum of Bernoulli random variables andUλa Poisson random variable having the same meanλ = EW.Using the Stein-Chen method and suitable couplings, general upper bounds for the variational distance betweenWandUλare given. These bounds are applied to problems of occupancy, using sampling with and without replacement and Pólya sampling, of capture-recapture, of spacings and of matching and ménage.Keywords
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