Calibrated FFT-based density approximations for α-stable distributions

Christian Menn, Svetlozar T. Rachev

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


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
Issue number8
StatePublished - Apr 10 2006


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

Fingerprint Dive into the research topics of 'Calibrated FFT-based density approximations for α-stable distributions'. Together they form a unique fingerprint.

Cite this