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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.
https://hal.archives-ouvertes.fr/hal-01521300
Contributor : Olivier Marchal Connect in order to contact the contributor
Submitted on : Friday, January 26, 2018 - 11:54:56 AM
Last modification on : Wednesday, November 3, 2021 - 5:59:23 AM
Contributor : Olivier Marchal Connect in order to contact the contributor
Submitted on : Friday, January 26, 2018 - 11:54:56 AM
Last modification on : Wednesday, November 3, 2021 - 5:59:23 AM