Mathematica 9 is now available
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Wolfram Mathematica Documentation Center
DOCUMENTATION CENTER SEARCH
New to Mathematica? Find your learning path »
Mathematica > Data Manipulation > Statistical Data Analysis > Probability & Statistics > Parametric Statistical Distributions > Heavy Tail Distributions > LevyDistribution >
Mathematica > Mathematics and Algorithms > Statistical Data Analysis > Probability & Statistics > Parametric Statistical Distributions > Heavy Tail Distributions > LevyDistribution >
BUILT-IN MATHEMATICA SYMBOLSee Also »|More About »

LevyDistribution

LevyDistribution
represents a Lévy distribution with location parameter and dispersion parameter .
MORE INFORMATION
  • The probability density for value in a Lévy distribution is proportional to .  »
  • The Lévy distribution LevyDistribution is a special case of the inverse gamma distribution with and . »
  • LevyDistribution allows to be any real number and to be any positive real number.
EXAMPLESCLOSE ALL
Basic Examples   (4)
Probability density function:
Cumulative distribution function:
Mean and variance of a Lévy distribution are infinite:
Median:
Probability density function:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=
 
Cumulative distribution function:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=
 
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]=
 
Median:
In[1]:=
Click for copyable input
Out[1]=
Scope   (5)
Generate a set of pseudorandom numbers that are Lévy distributed:
Compare its histogram to the PDF:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Compare a density histogram of the sample with the PDF of the estimated distribution:
Moments of order do not exist:
Generalized moments exist for order :
Hazard function:
Quantile function:
Applications   (1)
Find the full width at half-maximum of the van der Waals spectral profile:
Compute the location of the maximum:
Solve for the half-maximum points:
Find the width:
The frequency of the emitted particle is more likely to be greater than the mode:
Properties & Relations   (8)
Parameter influence on the CDF for each :
Lévy distribution is closed under translation and scaling by a positive factor:
Lévy distribution is closed under addition:
Relationships to other distributions:
Lévy distribution is a special case of type 5 PearsonDistribution:
Lévy distribution is a transformation of a NormalDistribution:
With scale:
Lévy distribution is a StableDistribution:
Possible Issues   (2)
LevyDistribution is not defined when is not a real number:
LevyDistribution is not defined when 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
Format:   HTML  |  CDF