Chi Distribution
The chi (χ) distribution with n degrees of freedom models the distribution of the square root of the sum of the squares of n independent normal variables. Alternatively, it is the distribution of the norm of a vector of n independent normal variables.
The chi distribution is closely related to the chi square distribution. A the square root of a variable with a chi square distribution has a chi distribution.
Special cases of the chi distribution include the Rayleigh distribution (2 degrees of freedom) and the Maxwell distribution (3 degrees of freedom.
The chi 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:
$$f(x) = \frac{x^{n-1}e^{-x^2/2}}{\Gamma(\frac{1}{2}n)2^{n/2-1}}$$where n is the degrees of freedom.
The chi distribution is implemented by the ChiDistribution class. It has one constructor which takes the degrees of freedom as its only argument. The following constructs a chi distribution with 10 degrees of freedom:
var chi = new ChiDistribution(10);The ChiDistribution class has one specific property, DegreesOfFreedom, that returns the degrees of freedom of the distribution.
ChiDistribution 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 Pcg32();
double sample = ChiDistribution.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..