The Generalized Pareto distribution is a generalization of the The Pareto Distribution
often used in risk analysis.
The Pareto distribution has a location parameter which corresponds to the
smallest possible value of the variable, a scale parameter which must be
strictly greater than 0, and a shape parameter.
The probability density function is:
The Generalized Pareto distribution is implemented by the ParetoDistribution
class. It has one constructor with
three arguments. The first argument is the shape parameter. The second and third arguments are
the scale and location parameters, respectively.
The following constructs the Generalized Pareto distribution with shape parameter -0.2, scale parameter 3, and location parameter 4.5:
var pareto = new GeneralizedParetoDistribution(-0.2, 3, 4.5);
Dim pareto = New GeneralizedParetoDistribution(-0.2, 3, 4.5)
No code example is currently available or this language may not be supported.
let pareto = GeneralizedParetoDistribution(-0.2, 3.0, 4.5)
The GeneralizedParetoDistribution class has three specific properties, ShapeParameter,
ScaleParameter, and
LocationParameter,
which return the shape, scale and location parameters of the distribution.
GeneralizedParetoDistribution has one static (Shared in Visual Basic) method, Sample, which generates a
random sample using a user-supplied uniform random number generator. The second, third and fourth arguments are the
shape, scale and location parameters of the distribution.
var random = new MersenneTwister();
double sample = GeneralizedParetoDistribution.Sample(random, -0.2, 3, 4.5);
Dim random = New MersenneTwister()
Dim sample = GeneralizedParetoDistribution.Sample(random, -0.2, 3, 4.5)
No code example is currently available or this language may not be supported.
let random = MersenneTwister()
let sample = GeneralizedParetoDistribution.Sample(random, -0.2, 3.0, 4.5)
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..