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Let W be a sum of Bernoulli random variables and U λ a Poisson random variable having the same mean λ = EW. Using the Stein-Chen method and suitable couplings, general upper bounds for the variational distance between W and U λ are 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.
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Barbour et al. (1989) studied this question.
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