- Extreme Optimization
- Documentation
- Statistics Library User's Guide
- 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 F Distribution

## The Non-central F Distribution | Extreme Optimization Numerical Libraries for .NET Professional |

The non-central F distribution is a generalization of the F distribution. It is the distribution of the quotient of a non-central chi-square variable and a (central) chi-square variable.

The non-central F distribution has three parameters. The first two are the degrees of freedom of the numerator and of the denominator. They must be strictly positive and are most commonly integers but this is not a requirement. The third parameter is the non-centrality parameter, which must be 0 or positive.

The probability density function (PDF) of the non-central F distribution is:

where ν_{1} is the degrees of freedom of the numerator,
ν_{2} is the degrees of freedom of the denominator,
and λ is the non-centrality parameter.

The non-central F distribution is implemented by the NonCentralFDistribution class. It has one constructor which takes the three parameters mentioned above as arguments. The following constructs a non-central F distribution with 4 degrees of freedom for the numerator, and 25 degrees of freedom for the denominator, and non-centrality parameter 15:

The NonCentralFDistribution class has three specific properties. NumeratorDegreesOfFreedom and DenominatorDegreesOfFreedom return the degrees of freedom of the numerator and the denominator, respectively. 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..

#### Other Resources

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.