Inverse Chi Square Distribution

The inverse chi square (χ2) distribution or inverted chi square distribution with n degrees of freedom models the distribution of the reciprocal (inverse) of a chi square variable, which is the sum of the squares of n independent normal variables. It is used in Bayesian statistics.

The inverse 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:

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

where ν is the degrees of freedom.

The inverse chi square distribution is implemented by the InverseChiSquareDistribution class. It has one constructor which takes the degrees of freedom as its only argument. The following constructs an inverse chi square distribution with 10 degrees of freedom:

C# 
var invChiSquare = new ChiSquareDistribution(10);

The InverseChiSquareDistribution class has one specific property, DegreesOfFreedom, that returns the degrees of freedom of the distribution.

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

See Also