New results on the sum of two generalized Gaussian random variables

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

18 Scopus citations

Abstract

We propose in this paper a new method to compute the characteristic function (CF) of the 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 result, 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 sumare analyzed and computed. Due to the complexity of the 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 a 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 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1017-1021
Number of pages5
ISBN (Electronic)9781479975914
DOIs
StatePublished - Feb 23 2016
EventIEEE Global Conference on Signal and Information Processing, GlobalSIP 2015 - Orlando, United States
Duration: Dec 13 2015Dec 16 2015

Publication series

Name2015 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2015

Conference

ConferenceIEEE Global Conference on Signal and Information Processing, GlobalSIP 2015
Country/TerritoryUnited States
CityOrlando
Period12/13/1512/16/15

Keywords

  • Generalized Gaussian
  • PDF approximation
  • characteristic function
  • cumulant
  • kurtosis
  • moment
  • sum of two random variables

ASJC Scopus subject areas

  • Information Systems
  • Signal Processing

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