Some applications of the Stein-Chen method for proving Poisson convergence

Let W be a sum of Bernoulli random variables and U. a Poisson random variable having the same mean . = EW. Using the Stein-Chen method and suitable couplings, general upper bounds for the variational distance between W and U. 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.