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 Cauchy Distribution

The Cauchy Distribution

Extreme Optimization Numerical Libraries for .NET Professional

The Cauchy distribution can be used to model the distribution of horizontal distances at which a line segment tilted at a random angle cuts a line.

The Cauchy distribution has one scale parameter. The probability density function is:

Probability density of the Cauchy distribution.

The Cauchy distribution looks similar to a normal distribution, but has a much heavier tail. It can be used to study hypothesis tests that assume a normal distribution. How well the tests perform on data from a Cauchy distribution gives a good indication of the sensitivity of the test to heavy-tail departures from normality.

The mean and standard deviation of the Cauchy distribution are undefined. This means that no amount of data points will yield a more accurate or reliable estimate of the mean and standard deviation than does a single point.

The Cauchy distribution is sometimes called the Lorentzian distribution.

The Cauchy distribution is implemented by the CauchyDistribution class. It has one constructor which takes the scale parameter as its only argument. The following constructs a beta distribution with scale parameter 3.2:

C#
VB
C++
F#
Copy
var cauchy = new CauchyDistribution(3.2);
Dim cauchy = New CauchyDistribution(3.2)

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

let cauchy = CauchyDistribution(3.2)

The CauchyDistribution class has one specific property, ScaleParameter, that returns the scale parameter of the distribution.

CauchyDistribution has one static (Shared in Visual Basic) method, Sample, which generates a random sample using a user-supplied uniform random number generator.

C#
VB
C++
F#
Copy
var random = new MersenneTwister();
double sample = CauchyDistribution.Sample(random, 3.2);
Dim random = New MersenneTwister()
Dim sample = CauchyDistribution.Sample(random, 3.2)

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

let random = MersenneTwister()
let sample = CauchyDistribution.Sample(random, 3.2)

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.