Notes for Intel® oneAPI Math Kernel Library Vector Statistics

ID 772987
Date 12/04/2020
Document Table of Contents

Two-Level Testing

To test K subsequences u1, u2, ..., un; un +1, un +2, ..., u2n; ...; u(K-1)n+1, u(K -1)n+2, ..., uKn of the original sequence, p-values p1, p2, ..., pK are computed. Since the resulting p-values for the sequence u1, u2, ..., uKn 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 q1 of the second level. Repeating this procedure L times results in obtaining L p-values of the second level q1, q2, ... , qL on which you can perform threshold testing.

We have conducted threshold second level testing for the VS generators with ten iterations (L=10) and applied the Kolmogorov-Smirnov goodness-of-fit test with Anderson-Darling statistics to evaluate p1, p2, ..., pK uniformity.