Generalized Gaussian mixture model

The parameters estimation of mixture distributions is an important task in statistical signal processing, Pattern recognition, blind equalization and other modern statistical tasks often call for mixture estimation. This paper aims to provide a realistic distribution based on Mixture of Generalized Gaussian distribution (MGG), which has the advantage to characterize the variability of shape parameter in each component in the mixture. We propose a formulation of the Expectation Maximization (EM) algorithm under Generalized Gaussian distribution. For this, two different methods are proposed to include the shape parameter estimation. In the first method a derivation of the Likelihood function is used to update the mixture parameters. In the second approach we propose an extension of the “classical” (EM) algorithm and to estimate the shape parameter in terms of Kurtosis. The Kullback-Leibler divergence (KLD) is used to compare, and evaluate these algorithms of MGG parameters estimation. An application of this technique is considered for modeling load distribution which exhibits an heterogeneity with a high variability of shape parameters ¹.