Optimal sub-Gaussian variance proxy for 3-mass distributions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912633540575232 |
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| author | Atouani, Soufiane Marchal, Olivier Arbel, Julyan |
| author_facet | Atouani, Soufiane Marchal, Olivier Arbel, Julyan |
| contents | We investigate the problem of characterizing the optimal variance proxy for sub-Gaussian random variables,whose moment-generating function exhibits bounded growth at infinity. We apply a general characterization method to discrete random variables with equally spaced atoms. We thoroughly study 3-mass distributions, thereby generalizing the well-studied Bernoulli case. We also prove that the discrete uniform distribution over $N$ points is strictly sub-Gaussian. Finally, we provide an open-source Python package that combines analytical and numerical approaches to compute optimal sub-Gaussian variance proxies across a wide range of distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06132 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal sub-Gaussian variance proxy for 3-mass distributions Atouani, Soufiane Marchal, Olivier Arbel, Julyan Statistics Theory We investigate the problem of characterizing the optimal variance proxy for sub-Gaussian random variables,whose moment-generating function exhibits bounded growth at infinity. We apply a general characterization method to discrete random variables with equally spaced atoms. We thoroughly study 3-mass distributions, thereby generalizing the well-studied Bernoulli case. We also prove that the discrete uniform distribution over $N$ points is strictly sub-Gaussian. Finally, we provide an open-source Python package that combines analytical and numerical approaches to compute optimal sub-Gaussian variance proxies across a wide range of distributions. |
| title | Optimal sub-Gaussian variance proxy for 3-mass distributions |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2510.06132 |