# 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:
- 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:
- Issue Date:
- 2015
- Type:
- Article

- Appears in Collections:
- Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

# Full metadata record

DC Field | Value | Language |
---|---|---|

dc.contributor.author | Soury, Hamza | en |

dc.contributor.author | Alouini, Mohamed-Slim | en |

dc.date.accessioned | 2015-05-31T14:04:50Z | en |

dc.date.available | 2015-05-31T14:04:50Z | en |

dc.date.issued | 2015 | en |

dc.identifier.uri | http://hdl.handle.net/10754/556078 | en |

dc.description.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. | en |

dc.language.iso | en | en |

dc.subject | Generalized Gaussian | en |

dc.subject | sum of two random variables | en |

dc.subject | characteristic function | en |

dc.subject | kurtosis | en |

dc.subject | moment | en |

dc.subject | cumulant | en |

dc.subject | PDF approximation | en |

dc.title | New Results On the Sum of Two Generalized Gaussian Random Variables | en |

dc.type | Article | en |

dc.contributor.department | Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division | en |

dc.eprint.version | Pre-print | en |

dc.contributor.affiliation | King Abdullah University of Science and Technology (KAUST) | en |

All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.