Calibrated FFT-based density approximations for -stable distributions

摘要: An algorithm for the approximation of @a-stable densities is developed and compared with similar methodologies. The proposed approach employs an adaptive Simpson rule quadrature Fourier inversion integral asymptotic Bergstrom series expansions tails density. It guaranteed that integrates precisely to unity which helpful numerical maximum-likelihood routines. accuracy has been verified respect values obtained by Nolan's program STABLE a grid parameter values. shown significant reduction computational effort can be achieved while maintaining satisfying accuracy.