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

# PowerDistribution

 PowerDistribution represents a power distribution with domain parameter k and shape parameter a.
• The probability density for value in a power distribution is proportional to for and zero otherwise.
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 power 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 depends only on the shape parameter:
Limiting values:
Kurtosis depends only on the shape parameter:
Limiting values:
Kurtosis attains its minimum:
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)
Suppose the variance of a normal variate follows PowerDistribution defined on the unit interval. Find the resulting distribution:
Generate random variates:
Compare a sample histogram to the distribution density:
Parameter influence on the CDF for each :
Power distribution is closed under scaling by a positive factor:
Relationships to other distributions:
KumaraswamyDistribution simplifies to a special case of power distribution:
Power distribution is a transformation of ExponentialDistribution:
Power distribution is a distribution of an inverse of ParetoDistribution:
New in 8