Comment on "Universal relation between skewness and kurtosis in complex dynamics"

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Ahmet Celikoglu, Ugur Tirnakli

Abstract

In a recent paper [M. Cristelli, A. Zaccaria, and L. Pietronero, Phys. Rev. E 85, 066108 (2012)], the authors analyzed the relation between skewness and kurtosis for complex dynamical systems, and they identified two power-law regimes of non-Gaussianity, one of which scales with an exponent of 2 and the other with 4/3. They concluded that the observed relation is a universal fact in complex dynamical systems. In this Comment, we test the proposed universal relation between skewness and kurtosis with a large number of synthetic data, and we show that in fact it is not a universal relation and originates only due to the small number of data points in the datasets considered. The proposed relation is tested using a family of non-Gaussian distribution known as q-Gaussians. We show that this relation disappears for sufficiently large datasets provided that the fourth moment of the distribution is finite. We find that kurtosis saturates to a single value, which is of course different from the Gaussian case (K=3), as the number of data is increased, and this indicates that the kurtosis will converge to a finite single value if all moments of the distribution up to fourth are finite. The converged kurtosis value for the finite fourth-m...Continue Reading

References

Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·F CarusoA Rapisarda
Sep 28, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ahmet CelikogluSílvio M Duarte Queirós
Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·B Coutinho dos Santos, C Tsallis
Sep 26, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Matthieu CristelliLuciano Pietronero

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Citations

Jun 15, 2016·Physical Review. E·José M Medina, José A Díaz
Feb 14, 2021·Materials·Robert Owsiński, Adam Niesłony

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