Logarithmic Moments for Mixture of Symmetric Alpha Stable Modelling

Abstract

Mixture of symmetric alpha-stable (s alpha s) models can be used to model impulsive data with heavy-tailed distribution. Lack of closed-form expression for alpha-stable distributions is a challenge for efficient mixture modeling in current methods. In this letter, we present an analytical approach for novel solution of parameter estimation in s alpha s mixture models which improves the computational efficiency of the existing methods. In addition, by introducing a centro-symmetrization (CS) transform, we generalize the application of proposed method to non-centered skewed data as well. The proposed method employs the logarithmic moments of data in maximization of conditional expectation of log-likelihood and is called EMLM algorithm. The experimental results on the synthetic and real datasets show that EMLM outperforms current baseline models not only in terms of goodness of fit of model, but also by increasing the performance of down-stream applications such as classification.