Entropy-Based Random Number Evaluation

SYNOPTIC ABSTRACT

Previous work has shown how to test a simple hypothesis of uniformity on the interval (0, 1) by using spacings-based estimates of entropy. In this paper we use Monte Carlo methods to extend previous tables of critical points and power for such entropy tests to the large sample sizes likely to be desirable when evaluating the output of one or more random number generators. A comparison with asymptotic critical points and power is made. The results are used to evaluate a number of commonly used random number generators, which are of importance in such areas as bootstrapping. At least one random number generator is found unsuitable for use. Since a generator cycling on .00, .01, .02, …, .99 (to more digits) could have a sample entropy of nearly zero, this test is appropriate only for generators that pass other extensive testing, such as the TESTRAND tests (e.g., see Karian and Dudewicz (1991)).

Key Words and Phrases:

• Random number generators
• entropy-based tests for uniformity
• asymptotic normality
• Monte Carlo estimates of percentage points and power
• goodness of fit tests
• evaluation and comparison
• chi-square entropy tests