Generalization of the fractional Poisson distribution

A generalization of the Poisson distribution based on the generalized Mittag-Leffler function $E_{\alpha ,\beta }(\lambda )$ 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 $\beta$ is suggested.