A new tail bound for the sum of bounded independent random variables
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866909547832016896 |
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| author | Loper, Jackson Regier, Jeffrey |
| author_facet | Loper, Jackson Regier, Jeffrey |
| contents | We construct a new tail bound for the sum of independent random variables for situations in which the expected value of the sum is known and each random variable lies within a specified interval, which may be different for each variable. This new bound can be computed by solving a two-dimensional convex optimization problem. Simulations demonstrate that the new bound is often substantially tighter than Hoeffding's inequality for cases in which both bounds are applicable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17594 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new tail bound for the sum of bounded independent random variables Loper, Jackson Regier, Jeffrey Probability Statistics Theory We construct a new tail bound for the sum of independent random variables for situations in which the expected value of the sum is known and each random variable lies within a specified interval, which may be different for each variable. This new bound can be computed by solving a two-dimensional convex optimization problem. Simulations demonstrate that the new bound is often substantially tighter than Hoeffding's inequality for cases in which both bounds are applicable. |
| title | A new tail bound for the sum of bounded independent random variables |
| topic | Probability Statistics Theory |
| url | https://arxiv.org/abs/2503.17594 |