Alternative way to characterize a q-gaussian distribution by a robust heavy tail measurement

TL;DR

This paper introduces a robust statistical method using the medcouple to identify q-Gaussian distributions from empirical data, improving precision and requiring smaller samples, aiding the analysis of systems with heavy tails.

Contribution

The authors propose a novel tail weight measure based on the medcouple to accurately identify q-Gaussian distributions from empirical data, even with long memory.

Findings

The medcouple remains stable with long memory data.

The method achieves higher precision with smaller data samples.

It enables better identification of nonextensive physical phenomena.

Abstract

The q-Gaussians are a class of stable distributions which are present in many scientific fields, and that behave as heavy tailed distributions for an especific range of q values. The identification of these values, which are used in the description of systems, is sometimes a hard task. In this work the identification of a q-Gaussian distribution from empirical data was done by a measure of its tail weight using robust statistics. Numerical methods were used to generate artificial data, to find out the tail weight -- medcouple, and also to adjust the curve between medcouple and the q value. We showed that the medcouple value remains unchanged when the calculation is applied to data which have long memory. A routine was made to calculate the q value and its standard deviation, when applied to empirical data. It is possible to identify a q-Gaussian by the proposed methods with higher precision than in the literature for the same data sample, or as precise as found in the literature. However, in this case, it is required a smaller sample of data. We hope that this method will be able to open new ways for identifying physical phenomena that belongs to nonextensive frameworks.