On the sub-Gaussianity of the Beta and Dirichlet distributions - Archive ouverte HAL Access content directly
Journal Articles Electronic Communications in Probability Year : 2017

On the sub-Gaussianity of the Beta and Dirichlet distributions

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.
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Dates and versions

hal-01521300 , version 1 (26-01-2018)

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Olivier Marchal, Julyan Arbel. On the sub-Gaussianity of the Beta and Dirichlet distributions. Electronic Communications in Probability, 2017, 22 (paper no. 54), pp.1-14. ⟨10.1214/17-ECP92⟩. ⟨hal-01521300⟩
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