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 Beta Distribution

The Non-central Beta Distribution

Extreme Optimization Numerical Libraries for .NET Professional

The non-central Beta distribution is a generalization of the The Beta Distribution.

The non-central Beta distribution has two shape parameters, usually denoted by the Greek letters α and β, which must be strictly positive. It also has a non-centrality parameter that must be 0 or positive. It reduces to the standard beta distribution when the non-centrality parameter is zero. Its probability density function (PDF) is:

Non Central BetaPDF

For certain specific values of the parameters α and β, the beta distribution is equivalent to a simpler distribution. For α = β = 1, the beta distribution is equivalent to the uniform distribution. For α = 1 and β = 2, and α = 2 and β = 1, the beta distribution reduces to a triangular distribution. For α and β very large, the beta distribution approximates to the normal distribution.

The beta distribution is implemented by the NonCentralBetaDistribution class. It has one constructor that takes three arguments: the two shape parameters, α and β, followed by the non-centrality parameter. The following constructs a non-central beta distribution with α = 1.5, β = 0.8, and non-centrality parameter 2:

C#
VB
C++
F#
Copy
var ncBeta1 = new NonCentralBetaDistribution(1.5, 0.8, 2.0);
Dim ncBeta1 = New NonCentralBetaDistribution(1.5, 0.8, 2.0)

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

let ncBeta1 = NonCentralBetaDistribution(1.5, 0.8, 2.0)

The NonCentralBetaDistribution class has three specific properties that correspond to the parameters of the distribution. The Alpha and Beta properties return the shape parameters, α and β. The NonCentralityParameter property 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

The Beta 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.