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 parameters. The first parameter is the shape parameter. The second and third parameters 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:
| C# |
 Copy
|
ParetoDistribution pareto = new GeneralizedParetoDistribution(-0.2, 3, 4.5);
|
| Visual Basic |
Copy
|
Dim pareto As GeneralizedParetoDistribution = New GeneralizedParetoDistribution(-0.2, 3, 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 variate using a user-supplied uniform random number generator. The second, third and fourth parameters are the
shape, scale and location parameters of the distribution.
| C# |
Copy
|
MersenneTwister random = new MersenneTwister();
double variate = ParetoDistribution.GetRandomVariate(random, -0.2, 3, 4.5);
|
| Visual Basic |
Copy
|
Dim random As MersenneTwister = New MersenneTwister()
Dim variate As Double = ParetoDistribution.GetRandomVariate(random, -0.2, 3, 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
class.