Highly sensitive universal statistical test

In Maurer's universal statistical test and its variations including Coron's test to check the randomness of a binary sequence, the entropy of sequence is calculated from the repetition intervals of L-grams in the sequence, and the randomness is evaluated based on whether or not the entropy attains the maximum. However, since the derivative of the entropy is zero at the maximum, the deviation from the maximum cannot be detected with high sensitivity. In this paper, we propose a new universal statistical test, in which a given sequence is converted into the most sensitive one by changing bit `1' to `0' randomly in the sequence. By simulation, we show that the proposed universal statistical test can detect non-randomness much more sensitively than Maurer's and Coron's tests and T-complexity test.