Characteristic function based parameter estimation of skewed alpha-stable distribution: An analytical approach

Abstract

This paper introduces a new technique for analytical parameter estimation of skewed α-stable distribution with 1<α≤2. Stable distribution as a four-parameter non-Gaussian distribution is completely characterized by its characteristic function (CF). There are some serious limitations in parameter estimation of α-stable distribution due to the lack of closed-form expression for the general α-stable probability density function (PDF). The proposed estimator uses a hierarchical framework based on the skewed α-stable CF, and hence, allows a rapid estimation of parameters with high accuracy in real-time signal processing algorithms. In our scheme, only two values of α-stable CF, which has analytic formula, are utilized to estimate the parameters of α-stable density. In addition, the closed-form expression for estimating the required values of CF is derived. To provide a precise quantitative assessment, our proposed approach is compared with three other state-of-the-art estimators which have analytic formulas through a series of goodness-of-fit tests. Simulation results also demonstrate that the proposed method has a good accuracy both for the symmetric and non-symmetric (skewed) α-stable distributions. Furthermore, the advantage of the proposed CF based method becomes more evident through the experimental results obtained from the high-resolution SAR images.