Some characterizations of the uniform distribution with applications to random number generation


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 are 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. © 1992 Kluwer Academic Publishers.

Publication Title

Annals of the Institute of Statistical Mathematics