- 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 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:

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:

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..

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