## 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 language | English (US) |
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Title of host publication | 2015 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2015 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1017-1021 |

Number of pages | 5 |

ISBN (Electronic) | 9781479975914 |

DOIs | |

State | Published - Feb 23 2016 |

Event | IEEE Global Conference on Signal and Information Processing, GlobalSIP 2015 - Orlando, United States Duration: Dec 13 2015 → Dec 16 2015 |

### Publication series

Name | 2015 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2015 |
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### Conference

Conference | IEEE Global Conference on Signal and Information Processing, GlobalSIP 2015 |
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Country/Territory | United States |

City | Orlando |

Period | 12/13/15 → 12/16/15 |

### Bibliographical note

Publisher Copyright:© 2015 IEEE.

## Keywords

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

## ASJC Scopus subject areas

- Information Systems
- Signal Processing