New Results On the Sum of Two Generalized Gaussian Random Variables

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

11 Scopus citations

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.
Original languageEnglish (US)
Title of host publication2015 IEEE Global Conference on Signal and Information Processing (GlobalSIP)
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Print)978-1-4799-7591-4
DOIs
StatePublished - 2015

Fingerprint

Dive into the research topics of 'New Results On the Sum of Two Generalized Gaussian Random Variables'. Together they form a unique fingerprint.

Cite this