New Results On the Sum of Two Generalized Gaussian Random Variables

Handle URI:
http://hdl.handle.net/10754/556078
Title:
New Results On the Sum of Two Generalized Gaussian Random Variables
Authors:
Soury, Hamza; Alouini, Mohamed-Slim ( 0000-0003-4827-1793 )
Abstract:
We propose in this paper a new method to compute the characteristic function (CF) of generalized Gaussian (GG) random variable in terms of the Fox H function. The CF of the sum of two independent GG random variables is then deduced. Based on this results, the probability density function (PDF) and the cumulative distribution function (CDF) of the sum distribution are obtained. These functions are expressed in terms of the bivariate Fox H function. Next, the statistics of the distribution of the sum, such as the moments, the cumulant, and the kurtosis, are analyzed and computed. Due to the complexity of bivariate Fox H function, a solution to reduce such complexity is to approximate the sum of two independent GG random variables by one GG random variable with suitable shape factor. The approximation method depends on the utility of the system so three methods of estimate the shape factor are studied and presented.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Issue Date:
2015
Type:
Article
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorSoury, Hamzaen
dc.contributor.authorAlouini, Mohamed-Slimen
dc.date.accessioned2015-05-31T14:04:50Zen
dc.date.available2015-05-31T14:04:50Zen
dc.date.issued2015en
dc.identifier.urihttp://hdl.handle.net/10754/556078en
dc.description.abstractWe propose in this paper a new method to compute the characteristic function (CF) of generalized Gaussian (GG) random variable in terms of the Fox H function. The CF of the sum of two independent GG random variables is then deduced. Based on this results, the probability density function (PDF) and the cumulative distribution function (CDF) of the sum distribution are obtained. These functions are expressed in terms of the bivariate Fox H function. Next, the statistics of the distribution of the sum, such as the moments, the cumulant, and the kurtosis, are analyzed and computed. Due to the complexity of bivariate Fox H function, a solution to reduce such complexity is to approximate the sum of two independent GG random variables by one GG random variable with suitable shape factor. The approximation method depends on the utility of the system so three methods of estimate the shape factor are studied and presented.en
dc.language.isoenen
dc.subjectGeneralized Gaussianen
dc.subjectsum of two random variablesen
dc.subjectcharacteristic functionen
dc.subjectkurtosisen
dc.subjectmomenten
dc.subjectcumulanten
dc.subjectPDF approximationen
dc.titleNew Results On the Sum of Two Generalized Gaussian Random Variablesen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.eprint.versionPre-printen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
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