On the sub-Gaussianity of the Beta and Dirichlet distributions

Olivier Marchal 1 Julyan Arbel 2
2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : We obtain the optimal proxy variance for the sub-Gaussianity of Beta distributions, thus proving, and improving, a recent conjecture made by Elder (2016). We provide different proof techniques for the symmetrical (around its mean) case and the non-symmetrical case. The technique in the latter case relies on studying the ordinary differential equation satisfied by the Beta moment-generating function known as the confluent hypergeometric function. As a consequence, we also derive the optimal proxy variance for Dirichlet distributions.
Type de document :
Article dans une revue
Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2017, 22 (paper no. 54), pp.1-14. 〈https://projecteuclid.org/euclid.ecp/1507860211〉
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Contributeur : Olivier Marchal <>
Soumis le : vendredi 26 janvier 2018 - 11:54:56
Dernière modification le : mercredi 11 avril 2018 - 01:58:30

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  • HAL Id : hal-01521300, version 1
  • ARXIV : 1705.00048

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Olivier Marchal, Julyan Arbel. On the sub-Gaussianity of the Beta and Dirichlet distributions. Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2017, 22 (paper no. 54), pp.1-14. 〈https://projecteuclid.org/euclid.ecp/1507860211〉. 〈hal-01521300〉

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