  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.
