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
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)
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
properties return the shape parameters, α and β.
property returns the non-centrality parameter.
For details of the properties and methods common to all continuous distribution classes, see the topic on