One aspect of Poisson approximation is that the support of the random variable of interest is often finite while the support of the Poisson distribution is not. In this paper we will remedy this by examining truncated negative binomial (of which Poisson is a special limiting case) approximation, so as to match the two supports of both distributions, and show that this will lead to improvements ...

Poisson approximation, random graphs, Stein's method Poisson approximations for the counts of a given subgraph in large random graphs were accomplished using Stein's method by Barbour and others. Compound Poisson approximation results, on the other hand, have not appeared, at least partly because of the lack of a suitable coupling. We address that problem by introducing the concept of cluster d...

An information-theoretic development is given for the problem of compound Poisson approximation, which parallels earlier treatments for Gaussian and Poisson approximation. Nonasymptotic bounds are derived for the distance between the distribution of a sum of independent integervalued random variables and an appropriately chosen compound Poisson law. In the case where all summands have the same ...

Multivariate Poisson approximation of the length spectrum of random surfaces is studied by means of the Chen-Stein method. This approach delivers simple and explicit error bounds in Poisson limit theorems. They are used to prove that Poisson approximation applies to curves of length up to order o(log log g) with g being the genus of the surface.