Lévy Distribution
| F_k[P_N(k)](x)=F_k[exp(-N|k|^beta)](x), |
where F is the Fourier transform of the probability P_N(k) for N-step addition of random variables. Lévy showed that beta in (0,2) for P(x) to be nonnegative. The Lévy distribution has infinite variance and sometimes infinite mean. The case beta=1 gives a Cauchy distribution, while beta=2 gives a normal distribution.
The Lévy distribution is implemented in the Wolfram Language as LevyDistribution [mu, sigma].
See also
Cauchy Distribution, Lévy Flight, Normal DistributionExplore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Lévy Distribution." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LevyDistribution.html