Random Number Generation with the Method of Uniform Sampling: Very High Goodness of Fit and Randomness

Abstract

System models in general are developed to predict outcomes for given inputs. However, the models used in simulations necessarily involve random variables when knowledge of the system is probabilistic. Various optimization methods require randomly generated populations. Today, various pseudorandom and true random number generators (RNGs) are continually developed to improve performance in various fields of science, including mathematics, physics, and engineering. Here we propose two test metrics to measure the goodness of fit error and the quality of an RNG based on improved empirical cumulative distribution function (IECDF). An RNG based on the method of uniform sampling, MUS-RNG, is proposed and demonstrated to provide high goodness of fit and randomness which is shown to have very small error even for a set of 10. MUS-RNG is compared with various true and pseudo-RNGs and tested on both uniform and standard normal distributions. Two quantitative benchmarking tests are proposed. It is also observed that MUS-RNG is also very successful for discontinuous cumulative distribution functions. The comparative results show that MUS-RNG has very small goodness of fit error and is easy to implement. The algorithm has the potential to provide higher convergence in optimization problems and accuracy in statistical simulations.