The Chi Square Distribution

The chi square (χ2) 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 Testing Goodness-Of-Fit, and for the one sample Testing Variances of a sample. The chi square distribution is a special case of the 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:

Probability density of the Chi square distribution.

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 argument. The following constructs a chi square distribution with 10 degrees of freedom:

var chiSquare = 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, Sample, which generates a random sample using a user-supplied uniform random number generator.

var random = new MersenneTwister();
double sample = ChiSquareDistribution.Sample(random, 10);

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

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

See Also