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

Bernardo Nipoti; Julyan Arbel; Olivier Marchal

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

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arxiv 1909.07026 v2 pith:KIFDCFDF submitted 2019-09-16 math.ST stat.OTstat.TH

Julyan Arbel , Olivier Marchal , Bernardo Nipoti This is my paper · ORCID

classification math.STstat.OTstat.TH

keywords functionhurwitzzetabeta-exponentialdistributionapplicationchainconnection

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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 beta-exponential distribution.

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