Recognition of stable distribution with Levy index alpha close to 2

TL;DR

This paper presents a new testing method for recognizing alpha-stable Levy distributions with index near 2 in small samples, combining visual and statistical tests, and applies it to plasma turbulence data.

Contribution

It introduces a combined testing procedure for identifying Levy distributions close to Gaussian in small samples, validated on simulated and real plasma data.

Findings

The method effectively distinguishes Levy from Gaussian distributions in small samples.

Application to plasma data reveals a transition from Levy to Gaussian fluctuations during L-H transition.

Demonstrates the method's utility in analyzing complex physical phenomena.

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.