variate X given by is Lévy-distributed with location and scale . Here is the cumulative distribution function of the standard normal distribution. Applications The frequency of geomagnetic reversals appears to follow a Lévy distribution The time of hitting a single point, at distance from the starting point, by the Brownian motion has the Lévy distribution with . (For a Brownian motion with drift, this time may follow an inverse Gaussian distribution, which has the Lévy distribution as a limit.) The length of the path followed by a photon in a turbid medium follows the Lévy distribution. A Cauchy process can be defined as a Brownian motion subordinated to a process associated with a Lévy distribution. Footnotes Notes References - John P. Nolan's introduction to stable distributions, some papers on stable laws, and a free program to compute stable densities, cumulative distribution functions, quantiles, estimate parameters, etc. See especially An introduction to stable distributions, Chapter 1 External links Continuous distributions Probability distributions with non-finite variance Power laws Stable distributions Paul Lévy (mathematician)