Optimal sub-Gaussian variance proxy for 3-mass distributions

2025/10/07 by Soufiane Atouani, Olivier Marchal, Atouani, Soufiane +3
Computer Science · Environmental Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Point processes and geometric inequalities #Soil Geostatistics and Mapping #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2510.06132

openalex publication_date 2025/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Optimal sub-Gaussian variance proxy for truncated Gaussian and exponential random variables
• Concentration of Measure Inequalities in Information Theory, Communications and Coding (Second Edition)
• On the Concentration of the Missing Mass
• Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems
• Large deviations for Dirichlet processes and Poisson-Dirichlet distributions with two parameters
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