{"ID":2881701,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.12103","arxiv_id":"2508.12103","title":"Sub-Poisson distributions: Concentration inequalities, optimal variance proxies, and closure properties","abstract":"We introduce a nonasymptotic framework for sub-Poisson distributions with moment generating function dominated by that of a Poisson distribution. At its core is a new notion of optimal sub-Poisson variance proxy, analogous to the variance parameter in the sub-Gaussian setting. This framework allows us to derive a Bennett-type concentration inequality without boundedness assumptions and to show that the sub-Poisson property is closed under key operations including independent sums and convex combinations, but not under all linear operations such as scalar multiplication. We derive bounds relating the sub-Poisson variance proxy to sub-Gaussian and sub-exponential Orlicz norms. Taken together, these results unify the treatment of Bernoulli and Poisson random variables and their signed versions in their natural tail regime.","short_abstract":"We introduce a nonasymptotic framework for sub-Poisson distributions with moment generating function dominated by that of a Poisson distribution. At its core is a new notion of optimal sub-Poisson variance proxy, analogous to the variance parameter in the sub-Gaussian setting. This framework allows us to derive a Benne...","url_abs":"https://arxiv.org/abs/2508.12103","url_pdf":"https://arxiv.org/pdf/2508.12103v1","authors":"[\"Lasse Leskelä\",\"Ian Välimaa\"]","published":"2025-08-16T16:54:13Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.ST\"]","methods":"[]","has_code":false}