Research on Parameters Estimation and Application of Alpha-Stable Distributions

Non-Gaussian signal processing is a new signal processing field with the development of signal processing techniques in recent years. For the problem of various non-Gaussian signals and noises have distinct spiky and impulsive characteristics in practice,leading them deviate from Gaussian distribution,we focus on the Alpha stable distribution,which is a kind of generalized Gaussian distribution,has the statistical characteristics of nonGaussian and heavy tailed. Firstly,the definitions and basic theories of the Alpha stable distribution are discussed.Secondly,we compute the probability density function value to implement Fractional Lower Order Moment method and the Sample Quintiles' method easily. Finally,the Alpha stable distribution is used in Shanghai composite Index and Dow Jones Industrial Average,and the related parameters are estimated.