This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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# LandauDistribution

 LandauDistribution represents a Landau distribution with location parameter and scale parameter .
• The probability density for value in a Landau distribution is proportional to .25123989
Probability density function:
Cumulative distribution function:
Mean and variance are not defined:
Probability density function:
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Cumulative distribution function:
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Mean and variance are not defined:
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 Scope   (4)
Generate a set of pseudorandom numbers that are Landau 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:
Hazard function:
Quantile function:
 Applications   (2)
Charged particles are bombarding a very thin target. The energy loss spectrum is then described by LandauDistribution. Define Landau function :
Find the maximum of the Landau function:
Find the half-width of the Landau function:
For large arguments, the Landau function behaves as :
Lindhard's first-order approximations to the Landau function:
Second-order approximation:
Parameter influence on the CDF for each :
Landau distribution is closed under translation:
Relationships to other distributions:
Landau distribution is a StableDistribution:
Evaluate the density of LandauDistribution using its defining integral representation:
New in 8