# Chi Square Distribution

The chi square (χ^{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 Testing Goodness-Of-Fit,
and for the one sample Testing Variances 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:

$$f(x) = \frac{x^{n/2-1}e^{-x/2}}{\Gamma(\frac{1}{2}n)2^{n/2}}$$
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..