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Notice that the Riemann Zeta function is simply ζ(s, 1) = ζ(s). In the next section we provide a new family of distributions, the Zeta family, which is based on the Hurwitz Zeta function, and provide its characteristic function. We also show that the well known generalized gamma family of distributions is a special case of the proposed family. (Notice that the exponential power family of distributions, the gamma, Weibull, Maxwell-Boltzmann and chi-squared distributions are special cases of the GG family). In section 3 we derive the Esscher transform and premium, and in section 4 we provide the tail conditional moments and the tail conditional expectation for members of this family. A conclusion is provided in section 5.

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