On the sub-Gaussianity of the Beta and Dirichlet distributions

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 r...

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Bibliographic Details
Published inElectronic communications in probability Vol. 22; no. none; pp. 1 - 14
Main Authors Marchal, Olivier, Arbel, Julyan
Format Journal Article
LanguageEnglish
Published Institute of Mathematical Statistics (IMS) 01.01.2017
Subjects
Mathematics
Probability
Statistics
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Summary: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.
ISSN:1083-589X
1083-589X
DOI:10.1214/17-ECP92