A Note on the Quality of Random Variates
Generated by the Ratio of Uniforms Method
of pseudo-random numbers generated by the ratio
of uniforms methods using linear congruential generators (LCGs) as the
source of uniform random numbers is investigated in this paper.
Due to the two-dimensional lattice structure of LCGs there is always a
comparable large gap without a point in the one-dimensional
distribution of any ratio of uniforms method. Lower bounds for these
probabilities only depending on the modulus and the Beyer quotient
of the LCG are proved for the case that the Cauchy the normal or
the exponential distribution are generated. These bounds justify the
not to use the ratio of uniforms method combined with
Mathematics Subject Classification:
65C10 (Random Number Generation)
CR Categories and Subject Descriptors:
G.3 [Probability and Statistics]: Random number generation
ratio of uniforms method, linear congruential generator,
© ACM, (1994). This is the author's version of the work.
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Trans. Model. Comput. Simul. 4(1), 96-106.