New results on the sum of two generalized Gaussian random variables

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.