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

09/16/2019

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by   Julyan Arbel, et al.

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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.