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Licensed Unlicensed Requires Authentication Published by De Gruyter August 27, 2016

Generalization of the fractional poisson distribution

Richard Herrmann


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.


We thank A. Friedrich for valuable discussions.


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Received: 2015-3-10
Published Online: 2016-8-27
Published in Print: 2016-8-1

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