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
Article Information
Identifiers and Pagination:
Year: 2016Volume: 7
First Page: 53
Last Page: 62
Publisher Id: TOSPJ-7-53
DOI: 10.2174/1876527001607010053
Article History:
Received Date: 17/08/2016Revision Received Date: 31/08/2016
Acceptance Date: 01/09/2016
Electronic publication date: 27/12/2016
Collection year: 2016
© 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.
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.
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.
