Optimal sub-Gaussian variance proxy for 3-mass distributions

Fuente: arXiv
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Main Authors: Atouani, Soufiane, Marchal, Olivier, Arbel, Julyan
Format: Preprint
Published: 2025
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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