Ranking of the best random number generators via entropy-uniformity theory

A key need in modern computer-based science and technology is for a high-quality (pseudo-) random number generator. (E.g., this is required in simulation and Monte Carlo studies, statistical bootstrapping, most expert systems and artificial intelligence systems, computer physics, etc.) Hundreds of random number generators have been proposed in a wide-ranging literature. Of these, 39 have been tested using TESTRAND, a program containing the most extensive series of random number quality tests available. Of those 39 evaluated, 12 passed the tests. These generators are referred to in the literature as URN02, URN03, URN12, URN13, URN14, URN15, URN22, URN30, URN35, URN36, URN37, and URN39. Using techniques of statistics ranking and selection for random number generators, the authors rank these good generators from best on down based on their entropy vs. that of a uniform distribution. The present study also includes one generator which failed the TESTRAND tests (the infamous RANDU, or URN08) and the authors comment on flow and when additional generators can be added to the present framework.