On goodness-of-fit tests for multiple recursive random number generators

This paper considers the problem of reducing the computational time in testing uniformity for a full period multiple recursive generator (MRG). If a sequence of random numbers generated by a MRG is divided into even number of segments, say 2s, then the multinomial goodness-of-fit tests and the empirical distribution function goodness-of-fit tests calculated from the ith segment are the same as those of the (s + i)th segment. The equivalence properties of the goodness-of-fit test statistics for a MRG and its associated reverse and additive inverse MRGs are also discussed.