Extreme Optimization™: Complexity made simple.

Math and Statistics
Libraries for .NET

  • Home
  • Features
    • Math Library
    • Vector and Matrix Library
    • Statistics Library
    • Performance
    • Usability
  • Documentation
    • Introduction
    • Math Library User's Guide
    • Vector and Matrix Library User's Guide
    • Data Analysis Library User's Guide
    • Statistics Library User's Guide
    • Reference
  • Resources
    • Downloads
    • QuickStart Samples
    • Sample Applications
    • Frequently Asked Questions
    • Technical Support
  • Blog
  • Order
  • Company
    • About us
    • Testimonials
    • Customers
    • Press Releases
    • Careers
    • Partners
    • Contact us
Introduction
Deployment Guide
Nuget packages
Configuration
Using Parallelism
Expand Mathematics Library User's GuideMathematics Library User's Guide
Expand Vector and Matrix Library User's GuideVector and Matrix Library User's Guide
Expand Data Analysis Library User's GuideData Analysis Library User's Guide
Expand Statistics Library User's GuideStatistics Library User's Guide
Expand Data Access Library User's GuideData Access Library User's Guide
Expand ReferenceReference
  • Extreme Optimization
    • Features
    • Solutions
    • Documentation
    • QuickStart Samples
    • Sample Applications
    • Downloads
    • Technical Support
    • Download trial
    • How to buy
    • Blog
    • Company
    • Resources
  • Documentation
    • Introduction
    • Deployment Guide
    • Nuget packages
    • Configuration
    • Using Parallelism
    • Mathematics Library User's Guide
    • Vector and Matrix Library User's Guide
    • Data Analysis Library User's Guide
    • Statistics Library User's Guide
    • Data Access Library User's Guide
    • Reference
  • Statistics Library User's Guide
    • Statistical Variables
    • Numerical Variables
    • Statistical Models
    • Regression Analysis
    • Analysis of Variance
    • Time Series Analysis
    • Multivariate Analysis
    • Continuous Distributions
    • Discrete Distributions
    • Multivariate Distributions
    • Kernel Density Estimation
    • Hypothesis Tests
    • Appendices
  • Continuous Distributions
    • Continuous 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
    • Log-Logistic Distribution
    • The Lognormal Distribution
    • The Non-central Beta Distribution
    • The Non-central Chi Square Distribution
    • The Non-central F Distribution
    • The Non-central Student t 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 Gumbel Distribution

The Gumbel Distribution

Extreme Optimization Numerical Libraries for .NET Professional

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:

Probability density of the Gumbel (extreme value) distribution.

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:

C#
VB
C++
F#
Copy
var gumbel = new GumbelDistribution(6.8, 4.1);
Dim gumbel = New GumbelDistribution(6.8, 4.1)

No code example is currently available or this language may not be supported.

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.

C#
VB
C++
F#
Copy
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)

No code example is currently available or this language may not be supported.

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..

Copyright (c) 2004-2021 ExoAnalytics Inc.

Send comments on this topic to support@extremeoptimization.com

Copyright © 2004-2021, Extreme Optimization. All rights reserved.
Extreme Optimization, Complexity made simple, M#, and M Sharp are trademarks of ExoAnalytics Inc.
Microsoft, Visual C#, Visual Basic, Visual Studio, Visual Studio.NET, and the Optimized for Visual Studio logo
are registered trademarks of Microsoft Corporation.