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)
No code example is currently available or this language may not be supported.
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)
No code example is currently available or this language may not be supported.
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..