Why CHI2RDN and CHI2PDF accept non integer values in Statistics Toolbox 7.2 (R2009b)?

The documentation requests a degrees of freedom parameter as a positive integer:

The degrees of freedom parameters in V must be positive integers, and the values in X must lie on the interval [0 Inf].

If I use a non integer degrees of freedom parameter I don't get any error message and a number is given as output. Is this an expected behavior?

Answer 1

[MathWorks Support Team]

This is expected behavior.

For many applications, the chi-square distribution has a degrees of freedom parameter that is a count and therefore, should be an integer.

Despite this, the mathematical formula that defines this distribution does not explicitly require an integer. There are other applications where non-integral degrees of freedom arise naturally. One example of this is the Satterthwaite approximation that uses a chi-square approximation with a non-integer degrees of freedom parameter.

More specifically, the chi-square distribution can be considered as a generalization of the GAMMA function:

https://www.mathworks.com/help/matlab/ref/gamma.html

which can be extended to non integer values.