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Abstract: As well known, cumulant expansion is an alternative way to moment expansionto fully characterize probability distributions provided all the moments exist.If this is not the case, the so called escort mean values or q-moments havebeen proposed to characterize probability densities with divergent moments C.Tsallis et al, J. Math. Phys 50, 043303 2009. We introduce here a newmathematical object, namely the q-cumulants, which, in analogy to thecumulants, provide an alternative characterization to that of the q-moments forthe probability densities. We illustrate this new scheme on a recently proposedfamily of scale-invariant discrete probabilistic models A. Rodriguez et al, J.Stat. Mech. 2008 P09006; R. Hanel et al, Eur. Phys. J. B 72, 263268 2009having q-Gaussians as limiting probability distributions.



Author: Antonio Rodriguez, Constantino Tsallis

Source: https://arxiv.org/



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