Improving Poisson approximations through tilting and expansion

Random variables defined on the natural numbers may often be approximated by Poisson variables. Just as normal approximations may be improved by saddlepoint methods, Poisson approximations may be substantially improved by tilting and expansion. A finite population relative of the probability generating function turns out to be useful in this process. (C) 2002 Elsevier Science B.V. All rights reserved.