Table 5 For the specious randomness file based on two concatenated 24-bit number systems, the probability to get some value a, lower than the cumulative distribution function Eq. (19) is tabulated for different n-grams ≤24, using non-overlapping counting (column 2). We know that for \(n=1,2,3,4,6,8,12\) and 24, all n-grams occur equally frequently, therefore the sequence is skip-balanced for those n-values. In column 3 we tabulate the corresponding result when overlapping n-gram counting was used
n | \(P(2^{n}-1,a\leq \chi ^{2}_{1})\) (non-overlapping) | \(P(2^{n}-1,a\leq \chi ^{2}_{2})\) (overlapping) |
|---|---|---|
1 | 0 | 0 |
2 | 0 | 0.00050 |
3 | 0 | 0.000034 |
4 | 0 | 0.0000000080 |
5 | 0.13 | <10−15 |
6 | 0 | <10−15 |
7 | 0.0092 | <10−15 |
8 | 0 | <10−15 |
9 | 0.000091 | <10−15 |
10 | 0.00024 | <10−15 |
11 | 0.034 | <10−15 |
12 | 0 | <10−15 |
13 | 0.0041 | <10−15 |
14–24 | <10−6 | <10−15 |