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SOME CHARACTERIZATIONS OF THE UNIFORM DISTRIBUTION

WITH APPLICATIONS TO RANDOM NUMBER GENERATION

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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.

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