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The F Distribution
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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:
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FDistribution f = new FDistribution(4, 25); |
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Dim f As FDistribution = New FDistribution(4, 25) |
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,
GetRandomVariate, which generates a random variate
using a user-supplied uniform random number generator.
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MersenneTwister random = new MersenneTwister();
double variate = FDistribution.GetRandomVariate(random, 4, 25); |
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Dim random As MersenneTwister = New MersenneTwister()
Dim variate As Double = FDistribution.GetRandomVariate(random, 7.6) |
The above example uses the Mersenne
Twister to generate uniform random numbers.
For details of the properties and methods common to all
continuous distribution classes, see the topic on ContinuousDistribution
class.
Up: Continuous Probability Distributions Next: The Gamma Distribution Previous: The Exponential Distribution Contents
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