Journal
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
Volume 42, Issue 1, Pages 202-214Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03610918.2011.633728
Keywords
Lehmer random number generators; Manhattan distance; Marsaglia effect; Test of randomness
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This article considers the Marsaglia effect by proposing a new test of randomness for Lehmer random number generators. Our test is based on the Manhattan distance criterion between consecutive pairs of random numbers rather than the usually adopted Euclidian distance. We derive the theoretical distribution functions for the Manhattan distance for both overlapping (two dimensional) as well as non-overlapping cases. Extensive goodness-of-fit testing as well as empirical experimentation provides ample proof of the merits of the proposed criterion.
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