Levy distribution | Vose Software

Levy distribution

Format: Levy(c, a)


The Levy distribution, named after Paul Pierre Lévy, is one of the few distributions that are stable and that have probability density functions that are analytically expressible. The others are the normal distribution and the Cauchy distribution.


The Lévy distribution is sometimes used in financial engineering to model price changes because the distribution can take into account the leptokurtosis ('fat' tails) one sometimes empirically observes in price changes on financial markets.

ModelRisk functions added to Microsoft Excel for the Levy distribution

VoseLevy generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseLevyObject constructs a distribution object for this distribution.

VoseLevyProb returns the probability density or cumulative distribution function for this distribution.

VoseLevyProb10 returns the log10 of the probability density or cumulative distribution function.  

VoseLevyFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseLevyFitObject constructs a distribution object of this distribution fitted to data.

VoseLevyFitP returns the parameters of this distribution fitted to data.


Lévy distribution equations