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A generalization of the cumulant expansion. Application to a scale-invariant probabilistic model.
- Source :
-
Journal of Mathematical Physics . Jul2010, Vol. 51 Issue 7, p073301. 17p. 3 Charts, 10 Graphs. - Publication Year :
- 2010
-
Abstract
- As well known, cumulant expansion is an alternative way to moment expansion to fully characterize probability distributions provided all the moments exist. If this is not the case, the so-called escort mean values (or q-moments) have been proposed to characterize probability densities with divergent moments [C. Tsallis et al., J. Math. Phys. 50, 043303 (2009)]. We introduce here a new mathematical object, namely, the q-cumulants, which, in analogy to the cumulants, provide an alternative characterization to that of the q-moments for the probability densities. To illustrate the technical details of the procedure, we apply this new scheme to further study a recently proposed family of scale-invariant discrete probabilistic models [A. Rodríguez et al., J. Stat. Mech.: Theory Exp. 2008, P09006; R. Hanel et al., Eur. Phys. J. B 72, 263 (2009)] having q-Gaussians as limiting probability distributions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 51
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 52616543
- Full Text :
- https://doi.org/10.1063/1.3448944