Fast fourier transforms: a tutorial review and a state of the art
Signal Processing
Signal processing with alpha-stable distributions and applications
Signal processing with alpha-stable distributions and applications
Numerical approximation of the symmetric stable distribution and density
A practical guide to heavy tails
Computing the probability density function of the stable Paretian distribution
Mathematical and Computer Modelling: An International Journal
Maximum likelihood estimation of stable Paretian models
Mathematical and Computer Modelling: An International Journal
Bayesian inference for α-stable distributions: A random walk MCMC approach
Computational Statistics & Data Analysis
A survey on computing Lévy stable distributions and a new MATLAB toolbox
Signal Processing
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An algorithm for the approximation of @a-stable densities is developed and compared with similar approximation methodologies. The proposed approach employs an adaptive Simpson rule for the quadrature of the Fourier inversion integral and asymptotic Bergstrom series expansions for the tails of the density. It is guaranteed that the approximation integrates precisely to unity which is helpful for numerical maximum-likelihood routines. The accuracy of the algorithm has been verified with respect to the values obtained by Nolan's program STABLE for a grid of parameter values. It is shown that a significant reduction of the computational effort with respect to Nolan's program can be achieved while maintaining a satisfying accuracy.