Empirical Tests of an Additive Random Number Generator

Abstract

Several empirical tests were made of the apparent randomness of numbers generated by the additive process X _j = ( X _{j -1} + X _{j -n} ) mod 1, where the X's are positive fractions. The results show that the numbers are uniformly distributed on the unit interval and that there is no significant serial correlation in the sequence. However, for n < 16, a test of run lengths indicates nonrandomness. This difficulty can be overcome by discarding alternate numbers.