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

 MoyalDistribution represents a Moyal distribution with location parameter and scale parameter .
• The probability density for value in a Moyal distribution is proportional to .
Probability density function:
Cumulative distribution function:
Mean and variance:
Median:
Probability density function:
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Cumulative distribution function:
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Mean and variance:
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Median:
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 Scope   (6)
Generate a set of pseudorandom numbers that are Moyal 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:
Skewness and kurtosis are constant:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Hazard function:
Quantile function:
 Applications   (2)
MoyalDistribution was obtained as a steepest descent approximation to LandauDistribution:
Find half-width of MoyalDistribution:
Parameter influence on the CDF for each :
Moyal distribution is closed under translation and scaling by a positive factor:
Relationships to other distributions:
Moyal distribution is a transformation of a GammaDistribution:
Moyal distribution is a transformed ExpGammaDistribution:
New in 8