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 that takes two arguments. The first argument is the location parameter, and corresponds to the mode of the probability density function. The second argument is the scale parameter.

The following constructs the same Gumbel distribution with mode 6.8 and scale parameter 4.1:

var gumbel = new GumbelDistribution(6.8, 4.1);

Dim gumbel = New GumbelDistribution(6.8, 4.1)

let gumbel = 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, Sample, which generates a random sample using a user-supplied uniform random number generator. The second and third arguments are the location and scale parameters of the distribution.

var random = new MersenneTwister();
double sample = GumbelDistribution.Sample(random, 6.8, 4.1);

Dim random = New MersenneTwister()
Dim sample = GumbelDistribution.Sample(random, 6.8, 4.1)

let random = MersenneTwister()
let sample = GumbelDistribution.Sample(random, 6.8, 4.1)

The above example uses the MersenneTwister class to generate uniform random numbers.

For details of the properties and methods common to all continuous distribution classes, see the topic on continuous distributions..