Randomness tests for the method of uniform sampling quasi-random number generator (MUS-QRNG)

Random number generation is still an important research field in many scientific applications today. Cryptography, Monte Carlo simulations and commertial applications all rely on reference random data. Randomness tests and basic statistics share the same history. Randomness can be summarized as the unpredictability of future samples of a random number generator even in the presence of known all past values. Various randomness tests are developed and due to their individual contributions, usually a battery of tests are applied to verify a random number generator. In signal processing however, the error of a specific observed sample set to a given distribution could be much more important when it is used as the input for a system model. Recently, this distance of finite samples set to a given distribution is studied and a quantitative measure for quality is proposed. Multi run computations like Monte Carlo simulations, often rely on accurate statistical data for high repetibility. Otherwise when the data is not accurate, the results could often rely on the source of random data generator. Many runs are often required to gain a confidence in the presence of those variances. In this work, recently proposed quasi-random number generator utilizing method of uniform sampling (MUS) is tested using standard goodness-of-fitness tests. MUS-QRNG numbers are shown to have exact statistics and also their randomness test results are observed to be similar to well known reference generator of Matlab. MUS-QRNG is proposed for high quality random data generation.