{"ID":2859474,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.06132","arxiv_id":"2510.06132","title":"Optimal sub-Gaussian variance proxy for 3-mass distributions","abstract":"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.","short_abstract":"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, the...","url_abs":"https://arxiv.org/abs/2510.06132","url_pdf":"https://arxiv.org/pdf/2510.06132v1","authors":"[\"Soufiane Atouani\",\"Olivier Marchal\",\"Julyan Arbel\"]","published":"2025-10-07T17:07:56Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}