We study the problem of generalized uniformity testing [BC17] of a discrete probability distribution: Given samples from a probability distribution p over an unknown discrete domain Ω, we want to distinguish, with probability at least 2/3, between the case that p is uniform on some subset of Ω versus -far, in total variation distance, from any such uniform distribution. We establish tight bound...

Let U and V be independent random variables with continuous density function on the interval (0, 1). We describe families of functions g for which uniformity of U and V is equivalent to uniformity of g(U, V) on (0, 1). These results axe used to prescribe methods for improving the quality of pseudo-random number generators by making them closer in distribution to the U(0, 1) distribution.

When testing that a sample of n points in the unit hypercube [0, 1] comes from a uniform distribution, the Kolmogorov–Smirnov and the Cramér–von Mises statistics are simple and well-known procedures. To encompass these measures of uniformity, Hickernell introduced the so-called generalized Lp-discrepancies. These discrepancies can be used in numerical integration through Monte Carlo and quasi–M...

evaluating the performance of irrigation systems by providing the possibility of increasing irrigation efficiency in those systems is an important factor in the field of water resources management. in this study, the performance of three systems were evaluated, including linear move sprinkler irrigation systems in maize, sugar beet and alfalfa fields of magsal agro-industrial company which is l...