title: Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem.
abstract: 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.
authors.affiliation: Hugo Steinhaus Center, Department of Mathematics, Wroclaw University of Technology, Wroclaw, Poland.
authors.forename: Krzysztof
authors.initials: K
authors.lastname: Burnecki
authors.affiliation: Hugo Steinhaus Center, Department of Mathematics, Wroclaw University of Technology, Wroclaw, Poland.
authors.forename: Agnieszka
authors.initials: A
authors.lastname: Wylomanska
authors.affiliation: Akhiezer Institute for Theoretical Physics, National Science Center "Kharkov Institute of Physics and Technology", Kharkov, Ukraine.|Max-Planck Institute for Physics of Complex Systems, Dresden, Germany.|Institute for Physics and Astronomy, University of Potsdam, Potsdam, Germany.
authors.forename: Aleksei
authors.initials: A
authors.lastname: Chechkin
mesh_terms: D000465:Algorithms; D006801:Humans; D008962:Models, Theoretical; D016011:Normal Distribution; D011336:Probability