On the Hurwitz zeta function with an application to the exponential-beta distribution

Julyan Arbel 1 Olivier Marchal 2 Bernardo Nipoti 3
1 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 prove a monotonicity property of the Hurwitz zeta function which, in turn, translates into a chain of inequalities for polygamma functions of different orders. We provide a probabilistic interpretation of our result by exploiting a connection between Hurwitz zeta function and the cumulants of the exponential-beta distribution.
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Submitted on : Monday, December 9, 2019 - 2:56:50 PM
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Julyan Arbel, Olivier Marchal, Bernardo Nipoti. On the Hurwitz zeta function with an application to the exponential-beta distribution. 2019. ⟨hal-02400451⟩

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