Journal
COMPUTATIONAL STATISTICS & DATA ANALYSIS
Volume 50, Issue 8, Pages 1891-1904Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.csda.2005.03.004
Keywords
density approximation; fast Fourier transformation; stable distribution; Bergstrom expansion
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An algorithm for the approximation of alpha-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. (c) 2005 Elsevier B.V. All rights reserved.
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