A unification of some approaches to Poisson approximation
Hans-Jürgen Witte · Journal of Applied Probability · 1990
Let S n be a sum of independent random variables. For the approximation of S n by a Poisson random variable Y with the same mean, the complex analysis approaches based on generating functions and the semigroup approach are presented in a unified setting which permits us to refine Kerstan's complex analysis approach obtaining considerably sharper upper bounds for some metric distances of S n and Y. These results are applied to some special S n counting the records of an i.i.d. sequence of random variables which is important to various applied problems, for instance the secretary problem.