In this project we have assessed the 1-distributed, 2-distributed, and 3-distributed
properties of each RNG. A -distributed test is to estimate the
-dimensional
uniformity as mentioned in Section
. For 1-distributed,
is divided into 4096 equidistant intervals. For 2-distributed, the unit square
is divided into 64x64 equal sized cells. For 3-distributed, the unit cube is divided
into 16x16x16 equal sized cells. The tests for higher than one dimensional uniformity
are carried out exactly the same as for the one dimensional
case. All of these
tests are compared with
distribution with df=4095.
One closely related test called serial test is to use non-overlapping
-dimensional points
,
, ...,
,
. To
differentiate between these tests, in our experiments we call the tests discussed in
the previous paragraph ``1-D
test'', ``2-D
test (overlapping)'', and
``3-D
test (overlapping)'', and serial tests are
``2-D
test (non-overlapping)'' and ``3-D
test (non-overlapping)''.
In both cases, if the samples have high autocorrelation, the distribution of
-dimensional points will deviates greatly from
-dimensional uniformity for
.
So higher dimensional uniformity tests also provide an indirect check of the
assumption that the samples are independent.