Discriminating between light- and heavy-tailed distributions with limit theorem
- In this paper we propose an algorithm to distinguish between light- and heavy-tailed probability laws underlying random datasets. The idea of the algorithm, which is visual and easy to implement, is to check whether the underlying law belongs to the domain of attraction of the Gaussian or non-Gaussian stable distribution by examining its rate of convergence. The method allows to discriminate between stable and various non-stable distributions. The test allows to differentiate between distributions, which appear the same according to standard Kolmogorov-Smirnov test. In particular, it helps to distinguish between stable and Student's t probability laws as well as between the stable and tempered stable, the cases which are considered in the literature as very cumbersome. Finally, we illustrate the procedure on plasma data to identify cases with so-called L-H transition.
Author details: | Krzysztof BurneckiORCiD, Agnieszka Wylomanska, Aleksei ChechkinORCiDGND |
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URN: | urn:nbn:de:kobv:517-opus4-408172 |
ISSN: | 1866-8372 |
Title of parent work (English): | Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe |
Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (495) |
Publication type: | Postprint |
Language: | English |
Date of first publication: | 2019/01/17 |
Publication year: | 2015 |
Publishing institution: | Universität Potsdam |
Release date: | 2019/01/17 |
Tag: | convergence; edge turbulence; fluctuations; fractional dynamics; levy fight; power-law; scaling laws; stable laws; statistical-analysis; stochastic-process |
Issue: | 495 |
Number of pages: | 23 |
Source: | PLOS ONE 10 (2015) 12, Art. e0145604 DOI: 10.1371/journal.pone.0145604 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät |
DDC classification: | 5 Naturwissenschaften und Mathematik / 50 Naturwissenschaften / 500 Naturwissenschaften und Mathematik |
6 Technik, Medizin, angewandte Wissenschaften / 61 Medizin und Gesundheit / 610 Medizin und Gesundheit | |
Peer review: | Referiert |
Publishing method: | Open Access |
Grantor: | Public Library of Science (PLOS) |
License (German): | CC-BY - Namensnennung 4.0 International |