A new method was developed to calculate the characteristics of a type of random variable called generalized Gaussian. By combining two independent generalized Gaussian variables, the probability and distribution functions of their sum were determined using a special mathematical function. The statistics of this sum distribution were then analyzed. To simplify the calculations, the sum of the two variables can be approximated by a single generalized Gaussian variable with a specific shape factor. Three methods were explored to estimate this shape factor for practical applications.