Poisson approximation by coupling

Rinaldo B. Schinazi

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arXiv · 2605.01894

Poisson approximation by coupling

Rinaldo B. Schinazi

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Abstract

It is well known that a binomial $(n,p)$ can be approximated by a Poisson distribution with parameter $np$. The typical approach in undergraduate probability texts is to show a convergence result for the distribution of the binomial as $n$ goes to infinity and $np$ converges to some $\lambda$. In this note we use instead the coupling technique to show a much more general result. Moreover, we only use elementary results from probability.

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Rinaldo B. Schinazi. 2026-05-03. Poisson approximation by coupling. https://arxiv.org/abs/2605.01894

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