Poisson approximation by coupling
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913084623290368 |
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| author | Schinazi, Rinaldo B. |
| author_facet | Schinazi, Rinaldo B. |
| contents | 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 $λ$. In this note we use instead the coupling technique to show a much more general result. Moreover, we only use elementary results from probability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01894 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Poisson approximation by coupling Schinazi, Rinaldo B. Probability 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 $λ$. In this note we use instead the coupling technique to show a much more general result. Moreover, we only use elementary results from probability. |
| title | Poisson approximation by coupling |
| topic | Probability |
| url | https://arxiv.org/abs/2605.01894 |