Sub-Poisson distributions: Concentration inequalities, optimal variance proxies, and closure properties
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916902899548160 |
|---|---|
| author | Leskelä, Lasse Välimaa, Ian |
| author_facet | Leskelä, Lasse Välimaa, Ian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12103 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sub-Poisson distributions: Concentration inequalities, optimal variance proxies, and closure properties Leskelä, Lasse Välimaa, Ian Probability Statistics Theory 60E05, 60E15 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. |
| title | Sub-Poisson distributions: Concentration inequalities, optimal variance proxies, and closure properties |
| topic | Probability Statistics Theory 60E05, 60E15 |
| url | https://arxiv.org/abs/2508.12103 |