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

 KumaraswamyDistribution represents a Kumaraswamy distribution with shape parameters and .
• The probability density for value is proportional to for , and is zero elsewhere.
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 Kumaraswamy 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:
Kurtosis:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Hazard function has a bathtub shape for :
Quantile function:
 Applications   (1)
KumaraswamyDistribution can be used in hydrology; consider monthly water levels at Lake Mead:
According to the Arizona Game and Fish Department, the maximum lake level is 1229 feet:
Fit Kumaraswamy distribution into the data:
Compare the histogram of the data with the estimated distribution:
Find the probability that Lake Mead is below drought level (1125 feet):
Find the average water level in feet:
Simulate the water levels for the next three years (with respect to the drought level):
Parameter influence on the CDF for each :
Relationships to other distributions:
Kumaraswamy distribution is a transformation of a BetaDistribution:
Kumaraswamy distribution simplifies to a BetaDistribution:
Kumaraswamy distribution simplifies to a PowerDistribution:
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