SOME CHARACTERIZATIONS OF THE UNIFORM DISTRIBUTION WITH APPLICATIONS TO RANDOM NUMBER GENERATION

LIH-YUAN DENG AND E. OLUSEGUN GEORGE

Department of Mathematical Sciences, Memphis State University, Memphis, TN 38152, U.S.A.

(Received September 5, 1989; revised October 22, 1990)

Abstract. 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.

Key words and phrases: Characterization of uniform distribution, independence, pseudo-random number generator, fractional sum.