Industrial and Management Systems Engineering



Poor statistical qualities for the RANDU random number generator

Date of this Version



P. Savory (2010), “Poor statistical qualities for the RANDU random number generator”, Mathematica Software Demonstration, The Wolfram Demonstations Project. Available at:


The RANDU linear congruential uniform random number generator was used in the 1960s. It has become infamous since when generated uniform [U(0,1)] values are used three at a time in a 3-tuple (grouping of three successive uniform values from the generator), the generator is biased. Notably, it fails the spectral test for dimensions greater than 2. This Mathematica demonstration allows one to see the dependency among the three-dimensional lattice structure. When the 3-tuples are plotted, one can observe that they fall on one of fifteen hyperplanes in the three dimensional space. As a results, the U(0,1) are highly correlated and bias whatever context in which they are being used.