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
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 .