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

[摘要] 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.

[学科分类] 电力

[关键词] Hurwitz zeta function;Polygamma function;Beta-exponential distribution;Monotonicity;Cumulants