Generalization of the fractional poisson distribution
Copyright policy )Generalization of the fractional poisson distribution
A generalization of the Poisson distribution based on the generalized Mittag-Leffler function $E_{α, β}(λ)$ 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.
10 pages, 3 figures
Bell polynomials, Bell and Stirling numbers, Mathematics - Statistics Theory, Statistics Theory (math.ST), fractional calculus, Mittag-Leffler functions and generalizations, Stirling numbers, Fractional derivatives and integrals, FOS: Mathematics, Probability distributions: general theory, 26A33, fractional Poisson distribution, Mittag-Leffler functions
Bell polynomials, Bell and Stirling numbers, Mathematics - Statistics Theory, Statistics Theory (math.ST), fractional calculus, Mittag-Leffler functions and generalizations, Stirling numbers, Fractional derivatives and integrals, FOS: Mathematics, Probability distributions: general theory, 26A33, fractional Poisson distribution, Mittag-Leffler functions
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).12 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!