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arXiv · 1503.07187

Generalization of the fractional Poisson distribution

Richard Herrmann
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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.

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Richard Herrmann. 2015-03-10. Generalization of the fractional Poisson distribution. https://doi.org/10.1515/fca-2016-0045

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