Generalized Gaussian distributions in Fourier domain via Maximum Entropy Principle

In this paper, a new approach for reconstructing the wide variety of Generalized Gaussian distributions is proposed. In particular, in order to reconstruct the most rational approximation of the probability density function of these distributions, the Maximum Entropy Principle method is used. The main novelty of this approach consists in introducing values of the Characteristic Function, as constraints to which the entropy functional is subjected, in order to overcome the drawbacks linked to the use of integer order moments as constraints. The new method is tested for the reconstruction of both symmetric Generalized Gaussian distributions (μ = 0) and also non-symmetric distributions (μ ≠ 0) by means of a translation formula. Finally, numerical simulations are proposed to assess the accuracy and the engineering applicability of the approach.