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Parameter Estimation and Random Number Generation to Stable Distributions

In this paper a robust parameter estimation based on the method of moments called Probability Integral Transformation is represented. The method is used to determine the characteristic exponent α, the scale γ and location parameter δ of a univariate symmetric stable distribution simultaneously from a random sample. A simulation sequence is made to test the accuracy and robustness of the estimation. In the second part we describe algorithms to multivariate stable random number generation in case of a discrete spectral measure and in independent case using Zolotarev’s formula. The simulation results are illustrated.