The Non-central Beta Distribution

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:

var ncBeta1 = new NonCentralBetaDistribution(1.5, 0.8, 2.0);

Dim ncBeta1 = New NonCentralBetaDistribution(1.5, 0.8, 2.0)

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..