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# WignerSemicircleDistribution

 WignerSemicircleDistribution[r] represents a Wigner semicircle distribution with radius r centered at the origin. WignerSemicircleDistributionrepresents a Wigner semicircle distribution with radius r centered at a.
• The probability density for value in a Wigner semicircle distribution is proportional to for between and .
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 have Wigner semicircle distribution:
Compare its histogram to the PDF:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Compare the 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:
Closed form for symbolic order:
Hazard function:
Quantile function:
 Applications   (1)
Construct a Gaussian symmetric matrix:
Fit WignerSemicircleDistribution into the eigenvalues:
Compare the histogram of the eigenvalues with the PDF:
Parameter influence on the CDF for each :
The WignerSemicircleDistribution is closed under translation and scaling by a positive factor:
Relationships to other distributions:
Wigner semicircle distribution is a special case of type 1 PearsonDistribution:
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