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

Zinoviy Landsman; Udi Makov; Tomer Shushi

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

机译：基于Hurwitz Zeta函数的新型分布及其在风险管理中的应用

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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.

机译：本文基于Hurwitz zeta函数构造了一个新的分布族，其中包括新颖的分布以及重要的已知分布，例如正态分布，γ分布，Weibull分布，Maxwell-Boltzmann分布和指数幂分布。我们为该族提供第n个矩，Esscher变换和premium以及尾部条件矩。

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《The Open Statistics & Probability Journal》 |2017年第1期|共10页
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Zinoviy Landsman; Udi Makov; Tomer Shushi;
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中图分类各科教学法、教学参考书;
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3. The joint value distribution of the Riemann zeta function and Hurwitz zeta functions II [J] . Mishou H Archiv der Mathematik . 2008,第3期

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4. Further Results Related to Generalized Hurwitz-Lerch Zeta Function and their Applications [C] . Khalied Challab, M. Darus, F. Ghanim UKM FST Postgraduate Colloquium . 2016

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5. Calibration of multivariate generalized hyperbolic distributions using the EM algorithm, with applications in risk management, portfolio optimization and portfolio credit risk. [D] . Hu, Wenbo. 2005

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6. Bounds for a joint distribution function with fixed sub-distribution functions: Application to competing risks [O] . Arthur V. Peterson Jr. 1976

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7. A New Class of Distributions Based on Hurwitz Zeta Function with Applications for Risk Management [O] . Zinoviy Landsman, Udi Makov, Tomer Shushi 2016

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8. Probability and Statistics in Item Analysis and Classification Problems:An Expansion Principle for Distribution Functions with Applications to Student’s Statistic and the One-Dimensional Classification Statistic [R] . Gustav Elfving 1957

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

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