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The Chi-Square Distribution
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The Chi Square Distribution
The chi square (&967;2) distribution with
n degrees of freedom models the distribution of the sum of
the squares of n independent normal variables. It is best
known for its use in the chi-square
goodness-of-fit test, and for the one sample chi-square test for the
variance of a sample. The chi square distribution is a special
case of the gamma
distribution.
The chi square distribution has one parameter: the degrees of
freedom. This value is usually an integer, but this is not an
absolute requirement. The probability density function (PDF)
is:
where n is the degrees of freedom.
The chi square distribution is a special case of the gamma
distribution, with scale parameter 2 and shape parameter
n/2.
The chi square distribution is implemented by the
ChiSquareDistribution
class. It has one constructor which takes the degrees of freedom as
its only parameter. The following constructs a chi square
distribution with 10 degrees of freedom:
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ChiSquareDistribution chiSquare = new ChiSquareDistribution(10); |
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Dim chiSquare As ChiSquareDistribution = New ChiSquareDistribution(10) |
The ChiSquareDistribution class has one specific
property,
DegreesOfFreedom, that returns the degrees of freedom
of the distribution.
ChiSquareDistribution 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 = ChiSquareDistribution.GetRandomVariate(random, 10); |
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Dim random As MersenneTwister = New MersenneTwister()
Dim variate As Double = ChiSquareDistribution.GetRandomVariate(random, 10) |
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 Erlang Distribution Previous: The Cauchy Distribution Contents
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