The Open Mathematics, Statistics and Probability Journal

2016, 7 : 53-62
Published online 2016 December 27. DOI: 10.2174/1876527001607010053
Publisher ID: TOSPJ-7-53

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

Zinoviy Landsman , Udi Makov and Tomer Shushi, *

*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.