Generalization of the fractional Poisson distribution

author: R. 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.

reference: Fract. Calc. Appl. Anal. (2016) 19(4) 832-842