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Journal of Function Spaces
Volume 2016, Article ID 8384767, 3 pages
Research Article

A Characterization of Symmetric Stable Distributions

Department of Mathematics and Cybernetics, Wrocław University of Economics, Ulica Komandorska 118/120, 53-345 Wrocław, Poland

Received 29 December 2015; Revised 21 March 2016; Accepted 27 March 2016

Academic Editor: Gen Qi Xu

Copyright © 2016 Wiktor Ejsmont. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Characterization problems in probability are studied here. Using the characteristic function of an additive convolution we generalize some known characterizations of the normal distribution to stable distributions. More precisely, if a distribution of a linear form depends only on the sum of powers of the certain parameters, then we obtain symmetric stable distributions.