Mathematica 9 is now available
SEARCH MATHEMATICA 8 DOCUMENTATION
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Mathematica > Data Manipulation > Statistics > Statistical Distributions > Continuous Statistical Distributions >
Mathematica > Mathematics and Algorithms > Statistics > Statistical Distributions > Continuous Statistical Distributions >
Built-in Mathematica SymbolSee Also »|More About »

LevyDistribution

LevyDistribution[Mu, Sigma]
represents a Lévy distribution with location parameter Mu and dispersion parameter Sigma.
  • The probability density for value x in a Lévy distribution is proportional to ⅇ^(-sigma/(2(x-mu)))/(x-mu)^(3/2).  »
  • The Lévy distribution LevyDistribution[0, Sigma] is a special case of the inverse gamma distribution with and . »
  • LevyDistribution allows Mu to be any real number and Sigma to be any positive real number.
EXAMPLESCLOSE ALL
Basic Examples   (2)
The mean and variance of a Lévy distribution are infinite:
Probability density function:
The mean and variance of a Lévy distribution are infinite:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
 
Probability density function:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
Scope   (2)
Generate a set of pseudorandom numbers that are Lévy distributed:
The 0.75 quantile of a Lévy distribution with mu=1 and sigma=2:
Applications   (2)
Plot the cumulative distribution function of the random variable:
A contour plot as both x and Sigma are varied:
Properties & Relations   (3)
The probability density function integrates to unity:
Moments of a Lévy distribution are finite only when :
LevyDistribution[0, Sigma] is a special case of InverseGammaDistribution:
Possible Issues   (2)
LevyDistribution is not defined when Mu is not a real number:
LevyDistribution is not defined when Sigma is not a positive real number:
Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:
New in 7
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team