## Arbitrary Scaling

As we mentioned, the mean of vector is assumed to be equal to the degrees of freedom . If the reference hypothesis assumes a different mean value, then we can regard the feature transformation as having been applied to a scaled variable. This is easily handled by the change of values theorem. Let have the prescribed degrees of freedom, but mean . Then, we write that

where has the standard distribution with mean , and is the diagonal matrix with elements Then, we simply replace matrix with and solve the problem assuming has the standard distribution with mean .

Baggenstoss 2017-05-19