The F Distribution

The F distribution is most often used to model the ratio of two variances. It is the primary distribution that underlies Analysis of Variance (ANOVA). It is used to determine the significance of the variation due to one or more effects compared to the total variation in the sample.

The F distribution has two parameters: the degrees of freedom of the numerator and of the denominator. These parameters act as shape parameters. As the F distribution models a ratio of two quantities, it is not meaningful to have a location or scale parameter.

The F distribution is sometimes called the variance ratio distribution or the Fisher-Snedecor distribution.

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

where n is the degrees of freedom of the numerator, and m is the degrees of freedom of the denominator.

The F distribution is implemented by the FDistribution class. It has one constructor which has two parameters. The following constructs an F distribution with 4 degrees of freedom for the numerator, and 25 degrees of freedom for the denominator:

var f = new FDistribution(4, 25);

Dim f = New FDistribution(4, 25)

let f = FDistribution(4.0, 25.0)

The FDistribution class has two specific properties, DenominatorDegreesOfFreedom and NumeratorDegreesOfFreedom, which returns the parameters of the distribution.

FDistribution has one static (Shared in Visual Basic) method, Sample, which generates a random sample using a user-supplied uniform random number generator.

var random = new MersenneTwister();
double sample = FDistribution.Sample(random, 4, 25);

Dim random = New MersenneTwister()
Dim sample = FDistribution.Sample(random, 4, 25)

let random = MersenneTwister()
let sample = FDistribution.Sample(random, 4.0, 25.0)

The above example uses the MersenneTwister class to generate uniform random numbers.

For details of the properties and methods common to all continuous distribution classes, see the topic on continuous distributions..