Generalization of the fractional Poisson distribution

Abstract

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.

10 pages, 3 figures

References in corpus (1)

• Fractional processes: from Poisson to branching one

Cited by in corpus (2)

• A note on Hadamard fractional differential equations with varying coefficients and their applications in probability
• Emission Distribution for the quantas of Maxwell-Chern-Simon Gauge Field coupled to External Current