RESEARCH ARTICLE


A New Class of Distributions Based on Hurwitz Zeta Function with Applications for Risk Management



Zinoviy Landsman, Udi Makov, Tomer Shushi*
Department of Statistics, University of Haifa, Mount Carmel, 31905, Haifa, Israel


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© Landsman et al; Licensee Bentham Open

open-access license: This is an open access article licensed under the terms of the Creative Commons Attribution-Non-Commercial 4.0 International Public License (CC BY-NC 4.0) (https://creativecommons.org/licenses/by-nc/4.0/legalcode), which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.

* Address correspondence to this author at the Department of Statistics, University of Haifa, Mount Carmel, 31905, Haifa, Israel; Tel: +97254593134; E-mail: tomershushi@gmail.com


Abstract

This paper constructs a new family of distributions, which is based on the Hurwitz zeta function, which includes novel distributions as well important known distributions such as the normal, gamma, Weibull, Maxwell-Boltzmann and the exponential power distributions. We provide the n-th moment, the Esscher transform and premium and the tail conditional moments for this family.

Keywords: Hurwitz zeta function, Esscher transform, Esscher premium, Tail conditional moments, Tail conditional expectations.