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

Abstract

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.

Keywords

• Hurwitz zeta function
• Polygamma function
• Beta-exponential distribution
• Monotonicity
• Cumulants