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- Appendices

- Continuous Distributions
- Continuous Probability Distributions
- The Beta Distribution
- The Cauchy Distribution
- The Chi Square Distribution
- The Erlang Distribution
- The Exponential Distribution
- The F Distribution
- The Gamma Distribution
- The Generalized Pareto Distribution
- The Gumbel Distribution
- The Laplace Distribution
- The Logistic Distribution
- The Lognormal Distribution
- The Normal Distribution
- The Pareto Distribution
- The Rayleigh Distribution
- Student's t Distribution
- The Transformed Beta Distribution
- The Transformed Gamma Distribution
- The Triangular Distribution
- The Continuous Uniform Distribution
- The Weibull Distribution

- The Generalized Pareto Distribution

The Generalized Pareto Distribution | Extreme Optimization Numerical Libraries for .NET Professional |

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:

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 parameters are the
shape, scale and location parameters of the distribution.

MersenneTwister random = new MersenneTwister(); double sample = 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 continuous distributions..

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