Statistical Tests

Abstract

As we have already seen, theoretical tests such as the spectral test give global (structural) information mainly about the distribution properties of the entire period of linear congruential sequences as well asLS(2)sequences, whereas the discrepancy test is able to provide upper bounds for the deviation of a part of the period of these sequences from the uniform distribution. Although the concept of discrepancy is applicable in general to any pseudorandom sequences, it is difficult to obtain the exact value even for simple generators such as linear congruential sequences, except for the two-dimensional discrepancy of a small number of points. For other generators, it becomes more difficult to obtain even upper bounds for discrepancies in low dimensions.