Levy alpha-stable distributions
In probability theory, the Levy symmetric stable distribution depend on a scale c and exponent α. The symmetric stable probability distribution is defined by a Fourier transform,
- Failed to parse (PNG conversion failed; check for correct installation of latex, dvips, gs, and convert): p(x) = {1 \over 2 \pi} \int_{-\infty}^{+\infty} dt \exp(-it x - |c t|^\alpha)
There is no explicit solution for the form of p(x). For α = 1 the distribution reduces to the Cauchy distribution. For α = 2 it is a Gaussian distribution with 
. For α < 1 the tails of the distribution become extremely wide.
Based on GSL manual, used under GFDL.
Categories: Math stubs | Probability distributions