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arXiv · 1909.07026

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

Julyan Arbel·Olivier Marchal·Bernardo Nipoti
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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 beta-exponential distribution.

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Julyan Arbel, Olivier Marchal, Bernardo Nipoti. 2019-09-16. On the Hurwitz zeta function with an application to the beta-exponential distribution. https://arxiv.org/abs/1909.07026

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