Model Simulation And Parameter Estimation Of Alpha Stable Distribution

In practice,various non-gaussian signals and noises have distinct spiky and impulsive characteristics,the decay of its'probability density function is slower than the Gaussian distribution's,showing significant tails. The Alpha stable distribution, which bases on the broad Central Limit Theorem, has the statictical characteristics of non-Gaussian and heavy tailed. So it provides a strong theoretical tool for the analysis of the non-Gaussian signals. This thesis focuses on the modal simulation for the Alpha stable distribution and the estimation for its prameters.Firstly, this thesis gives the modal simulation for the Alpha stable distribution, because there is no closed-form expression for the probability density function of the Al- pha stable distribution, the FFT-based method for calculating the theoretical probability density is provided.Secondly, this thesis implements the Fractional Lower Order Moments method and the Log Moments method for the parameter estimation of the symmetrical distribution condition. For the asymmetrical condition, the Fractional Lower Order Moments method and the Log Moments method are extended to implement the estimation.This thesis also gives the estimation method based on the empirical characteristic function.Finally, the modal simulation of the isotropic clutter is given. And the parameter estimation for the isotropic clutter is also implemented.