Recognition of stable distribution with Levy index alpha close to 2

Abstract

We address the problem of recognizing alpha-stable Levy distribution with Levy index close to 2 from experimental data. We are interested in the case when the sample size of available data is not large, thus the power law asymptotics of the distribution is not clearly detectable, and the shape of empirical probability density function is close to a Gaussian. We propose a testing procedure combining a simple visual test based on empirical fourth moment with the Anderson-Darling and Jarque-Bera statistical tests and we check the efficiency of the method on simulated data. Furthermore, we apply our method to the analysis of turbulent plasma density and potential fluctuations measured in the stellarator type fusion device and demonstrate that the phenomenon of L-H transition occurring in this device is accompanied by the transition from Levy to Gaussian fluctuation statistics.

Accepted to PRE

References in corpus (3)

• The scaling laws of human travel
• Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime
• On the kinetic equation of linear fractional stable motion and applications to modeling the scaling of intermittent bursts

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