Calibrated FFT-based density approximations for α-stable distributions

Christian Menn, Svetlozar T. Rachev

Research output: Contribution to journalArticle

31 Scopus citations

Abstract

An algorithm for the approximation of α-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 Bergström 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.

Original languageEnglish
Pages (from-to)1891-1904
Number of pages14
JournalComputational Statistics and Data Analysis
Volume50
Issue number8
DOIs
StatePublished - Apr 10 2006

Keywords

  • Bergström expansion
  • Density approximation
  • Fast Fourier transformation
  • Stable distribution

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