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-Gaussi...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Public Library of Science (PLoS)
2015-01-01
|
| Series: | PLoS ONE |
| Online Access: | http://europepmc.org/articles/PMC4689533?pdf=render |
| _version_ | 1818949527805100032 |
|---|---|
| author | Krzysztof Burnecki Agnieszka Wylomanska Aleksei Chechkin |
| author_facet | Krzysztof Burnecki Agnieszka Wylomanska Aleksei Chechkin |
| author_sort | Krzysztof Burnecki |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T09:04:07Z |
| format | Article |
| id | doaj.art-f4581090773441e18413503842dd4c24 |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-12-20T09:04:07Z |
| publishDate | 2015-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-f4581090773441e18413503842dd4c242022-12-21T19:45:47ZengPublic Library of Science (PLoS)PLoS ONE1932-62032015-01-011012e014560410.1371/journal.pone.0145604Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem.Krzysztof BurneckiAgnieszka WylomanskaAleksei ChechkinIn 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.http://europepmc.org/articles/PMC4689533?pdf=render |
| spellingShingle | Krzysztof Burnecki Agnieszka Wylomanska Aleksei Chechkin Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem. PLoS ONE |
| title | Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem. |
| title_full | Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem. |
| title_fullStr | Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem. |
| title_full_unstemmed | Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem. |
| title_short | Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem. |
| title_sort | discriminating between light and heavy tailed distributions with limit theorem |
| url | http://europepmc.org/articles/PMC4689533?pdf=render |
| work_keys_str_mv | AT krzysztofburnecki discriminatingbetweenlightandheavytaileddistributionswithlimittheorem AT agnieszkawylomanska discriminatingbetweenlightandheavytaileddistributionswithlimittheorem AT alekseichechkin discriminatingbetweenlightandheavytaileddistributionswithlimittheorem |