Consider the transformation

Although dimension-preserving, the sign of the input
data is lost. This problem clearly belongs to the ``Gaussian"
row in Table 3.1 since the
associated energy statistic can indeed be
computed from . The PDF
is found
in the ``Gaussian" row in Table 3.1,
from which we have

Under , is a set of independent
Chi-square RV with one degree of freedom
(See Section 16.1.2), therefore,

Performing the calcellations in

we get

For more information, refer to the software module
`software/module_square.m`.
Re-synthesis of using UMS (Section 3.3) from
is accomplished by assigning

where sign takes a value of or , each with probability 1/2.
For more information, refer to the software module
`software/module_square_synth.m`.

Baggenstoss
2017-05-19