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The Gumbel Distribution
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The Gumbel Distribution
The Gumbel distribution can be used to model the extreme of
a number of values. Sports records, flood levels, and the magnitude
of earthquakes can all be modeled using this distribution.
The Gumbel distribution has a location parameter corresponding
to the mode of the distribution, and a scale parameter. The
probability density function is:
The Gumbel distribution is also known as the extreme value
distribution or the log-Weibull distribution.
The Gumbel distribution is implemented by the GumbelDistribution
class. It has one constructor with two parameters. The first
parameter is the location parameter, and corresponds to the mode of
the probability density function. The second parameter is the scale
parameter.
The following constructs the same Gumbel distribution with mode
6.8 and scale parameter 4.1:
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GumbelDistribution gumbel = new GumbelDistribution(6.8, 4.1); |
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Dim gumbel As GumbelDistribution = New GumbelDistribution(6.8, 4.1) |
The GumbelDistribution class has two specific
properties,
LocationParameter and
ScaleParameter, which return the location parameter
(mode) and scale parameter of the distribution.
GumbelDistribution has one static (Shared
in Visual Basic) method,
GetRandomVariate, which generates a random variate
using a user-supplied uniform random number generator. The second
and third parameters are the location and scale parameters of the
distribution.
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MersenneTwister random = new MersenneTwister();
double variate = GumbelDistribution.GetRandomVariate(random, 6.8, 4.1); |
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Dim random As MersenneTwister = New MersenneTwister()
Dim variate As Double = GumbelDistribution.GetRandomVariate(random, 6.8, 4.1) |
The above example uses the Mersenne
Twister to generate uniform random numbers.
For details of the properties and methods common to all
continuous distribution classes, see the topic on ContinuousDistribution
class.
Up: Continuous Probability Distributions Next: The Laplace Distribution Previous: The Gamma Distribution Contents
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