Joint Parameters Estimation for General Alpha Stable Random Noise

This paper is concerned with the parameters estimation of i.i.d. random noise subjects to general Alpha stable distribution (αS) (include symmetrical and skewed distribution). We discuss the joint parameters estimation scheme for the αS random series. We firstly estimate the parameter α and σ by means of the Empirical Character Function (ECF) method. Using the deskewed transform, we next propose a new method to estimate the location parameter μ. Then, using the estimations of μ and α and with the Fractional Lower Order Moment (FLOM) method, an improved estimator of skewness parameter β is proposed. Furthermore, with the estimations of β and μ in the case of α=1 employing ECF method, a hybrid joint estimation scheme of four parameters is presented. The simulation results show that the proposed method performs well on wide region of α in estimating β and μ in comparison with traditional ECF method.