Asymptotic representation for PDF of Alpha stable distribution
Xutao Li · Journal of Circuits and Systems · 2009
No closed-form expressions exist for general stable density function and distribution functions,except for several special distributions.The method using convergent series is shown to be numerical unstable and the number of series is not certain.The same shortage exists in the representation based on scale mixtures of Gaussians and the performance is worse.In this paper,we present a new method by means of the scale mixtures of only two Gaussians.And then the approach to calculate the mixture proportion and the scale parameters of two Gaussians is proposed.