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

# FrechetDistribution

 FrechetDistribution represents the Frechet distribution with shape parameter and scale parameter . FrechetDistributionrepresents the Frechet distribution with shape parameter , scale parameter , and location parameter .
• The Frechet distribution gives the asymptotic distribution of the maximum value in a sample from a distribution such as the Cauchy distribution.
• The probability density for value in a Frechet distribution is proportional to for and zero otherwise.
• The probability density for value in a Frechet distribution with location parameter is proportional to for and zero otherwise.
Probability density function:
With location parameter:
Cumulative distribution function:
With location parameter:
Mean:
Variance:
Median:
Probability density function:
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With location parameter:
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Cumulative distribution function:
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With location parameter:
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Mean:
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Variance:
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Median:
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 Scope   (7)
Generate a set of pseudorandom numbers that are Frechet 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:
Skewness depends only on the first parameter:
Limiting values:
Kurtosis depends only on the first parameter:
Limiting values:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Hazard function:
With location parameter:
Quantile function:
With location parameter:
 Applications   (2)
According to a study, the annual maximal tephra (solid material) volume in volcanic eruptions follows a FrechetDistribution with shape parameter 0.71 and scale parameter 6.3, given in cubic kilometers:
Find median annual maximal tephra volume:
Find the average annual maximal tephra volume:
Find the mode of the distribution:
Find the probability that the annual maximal tephra volume is greater than 30 cubic kilometers:
Simulate the annual maximal tephra volume for the next 30 years:
FrechetDistribution can be used to model annual maximum wind speeds:
Fit the distribution into the data:
Compare the histogram of the data with the PDF of the estimated distribution:
Find the probability of annual maximum wind exceeding 90 km/h:
Find average annual maximum wind speed:
Simulate maximum wind speed for 30 years:
Parameter influence on the CDF for each :
Frechet distribution is closed under positive parameter scaling and translation:
The family of FrechetDistribution is closed under maximum:
CDF of FrechetDistribution solves the maximum stability postulate equation:
Fix and and simplify:
Relationships to other distributions:
The default location is 0:
Frechet distribution is a transformation of WeibullDistribution:
Frechet distribution is related to MaxStableDistribution:
Frechet distribution is related to MinStableDistribution:
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