A Characterization of Symmetric Stable Distributions

A Characterization of Symmetric Stable Distributions

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...

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Main Author: Wiktor Ejsmont
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2016/8384767
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spelling doaj-f336c626d52a427f8dd43f6001cb6d802020-11-24T20:59:17ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/83847678384767A Characterization of Symmetric Stable DistributionsWiktor Ejsmont0Department of Mathematics and Cybernetics, Wrocław University of Economics, Ulica Komandorska 118/120, 53-345 Wrocław, PolandCharacterization 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.http://dx.doi.org/10.1155/2016/8384767
collection DOAJ
language English
format Article
sources DOAJ
author Wiktor Ejsmont
spellingShingle Wiktor Ejsmont
A Characterization of Symmetric Stable Distributions
Journal of Function Spaces
author_facet Wiktor Ejsmont
author_sort Wiktor Ejsmont
title A Characterization of Symmetric Stable Distributions
title_short A Characterization of Symmetric Stable Distributions
title_full A Characterization of Symmetric Stable Distributions
title_fullStr A Characterization of Symmetric Stable Distributions
title_full_unstemmed A Characterization of Symmetric Stable Distributions
title_sort characterization of symmetric stable distributions
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2016-01-01
description 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.
url http://dx.doi.org/10.1155/2016/8384767
work_keys_str_mv AT wiktorejsmont acharacterizationofsymmetricstabledistributions
AT wiktorejsmont characterizationofsymmetricstabledistributions
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