On parameter estimation of symmetric alpha-stable distribution

In this paper, a novel approach has been proposed for estimating the parameters of symmetric alpha-stable distribution with 1 ≤ α ≤ 2. Alpha-stable distribution can model the statistical behavior of non-Gaussian heavy tailed signals and noises with impulsive components. There are some serious consideration in parameter estimation with stable random variable due to the lack of expression in analytic form for its distribution. In this method, the closed-form expression for parameter estimators is achieved by means of the values of characteristic function (CF) in two different points. We also establish a framework to determine these points in the general case. Performance comparison between the proposed method and the other methods is performed through several simulations and numerical results confirm that our method is efficient and has better performance even with a few number of samples.