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 Non-central Chi Square Distribution

The Non-central Chi Square Distribution

Extreme Optimization Numerical Libraries for .NET Professional

The non-central chi square (χ2) distribution with n degrees of freedom and non-centrality parameter λ is a generalization of the chi square distribution. It is used in the power analysis of statistical tests, including likelihood ratio tests.

The non-central chi square distribution has two parameters. The first is the degrees of freedom. This value is usually an integer, but this is not an absolute requirement. The second parameter is the non-centrality parameter. The probability density function (PDF) is:

Non Central Chi SquarePDF

where n is the degrees of freedom and λ is the non-centrality parameter.

The non-central chi square distribution is implemented by the NonCentralChiSquareDistribution class. It has one constructor which takes the degrees of freedom and the non-centrality parameter as arguments. The following constructs a non-central chi square distribution with 10 degrees of freedom and non-centrality parameter 15:

C#
VB
C++
F#
Copy
var ncChiSquare = new NonCentralChiSquareDistribution(10, 15);
Dim ncChiSquare = New NonCentralChiSquareDistribution(10, 15)

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

let ncChiSquare = NonCentralChiSquareDistribution(10.0, 15.0)

The NonCentralChiSquareDistribution class has two specific properties. DegreesOfFreedom returns the degrees of freedom of the distribution. NonCentralityParameter returns the non-centrality parameter.

For details of the properties and methods common to all continuous distribution classes, see the topic on continuous distributions..

See Also

Other Resources

Continuous Probability Distributions
The Chi Square distribution
The Non-central F Distribution

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.