Two-Level Testing
To test , , ..., on which you can perform threshold testing.
K
subsequences u
1
, u
2
, ..., u
n
; u
n+1
u
n+2
u
2
; ...; n
u
(K-1)n+1
, u
(K-1)n+2
, ..., u
Kn
of the original sequence, p-values p
1
, p
2
, ..., p
K
are computed. Since the resulting p-values for the sequence u
1
, u
2
, ..., u
Kn
of truly random numbers are supposed to be uniformly distributed over the interval (0, 1), a uniformity test can be performed for these p-values, returning p-value q
1
of the second level. Repeating this procedure L
times results in obtaining L
p-values of the second level q
1
, q
2
, ... , q
L
We have conducted threshold second level testing for the VS generators with ten iterations ( uniformity.
L
=10) and applied the Kolmogorov-Smirnov goodness-of-fit test with Anderson-Darling statistics to evaluate p
1
, p
2
, ..., p
K