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

# ExponentialPowerDistribution

 ExponentialPowerDistribution represents an exponential power distribution with shape parameter , location parameter , and scale parameter .
• The probability density for value in an exponential power 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   (7)
Generate a set of pseudorandom numbers that are exponential power distributed:
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:
Exponential power distribution is symmetric:
Kurtosis depends only on the shape parameter :
The limiting value for kurtosis:
Different moments with closed forms as functions of parameters:
Hazard function has a different shape depending on the parameter :
Quantile function:
 Applications   (1)
ExponentialPowerDistribution can be used as a smooth approximation to the distribution of the length of a random vector from DirichletDistribution:
Probability density function:
Create a sample:
Fit exponential power distribution into the data:
Compare the histogram of the sample with the PDFs of both distributions:
Compare means:
Parameter influence on the CDF for each :
Exponential power distribution is closed under translation and scaling by a positive factor:
ExponentialPowerDistribution can be narrower or wider than NormalDistribution, depending on the value of the shape parameter :
Relationships to other distributions:
LaplaceDistribution is a special case of exponential power distribution:
New in 8