Generalization of the fractional poisson distribution

  • 1 GigaHedron, Berliner Ring 80 D - 63303 Dreieich, Germany
Richard Herrmann

Abstract

A generalization of the Poisson distribution based on the generalized Mittag-Leffler function Eα,β(λ) is proposed and the raw moments are calculated algebraically in terms of Bell polynomials. It is demonstrated, that the proposed distribution function contains the standard fractional Poisson distribution as a subset. A possible interpretation of the additional parameter β is suggested.

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Fractional Calculus and Applied Analysis (FCAA) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order.

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