A note on the quality of random variates generated by the ratio of uniforms method

Wolfgang Hörmann

Publikation: Working/Discussion PaperWU Working Paper

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Abstract

The one-dimensional distribution 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 recommendation not to use the ratio of uniforms method combined with LCGs. (author's abstract)

Publikationsreihe

ReihePreprint Series / Department of Applied Statistics and Data Processing
Nummer5

WU Working Paper Reihe

  • Preprint Series / Department of Applied Statistics and Data Processing

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