The Non-central F Distribution

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 ν₁ is the degrees of freedom of the numerator, ν₂ 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:

var ncf = new NonCentralFDistribution(4, 25, 15.0);

Dim ncf = New NonCentralFDistribution(4, 25, 15.0)

let ncf = NonCentralFDistribution(4.0, 25.0, 15.0)

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..