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

Journal of inequalities and applications

article

Julyan Arbel¹  Olivier Marchal²  Bernardo Nipoti³ 

[1] Université Grenoble Alpes;Université Jean Monnet, Institut Camille Jordan, Université de Lyon;Department of Economics, Management and Statistics, Università degli Studi di Milano Bicocca

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

DOI  :  10.1186/s13660-020-02357-1

学科分类：电力

来源: SpringerOpen

【 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.

【 授权许可】

CC BY