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

Hörmann, Wolfgang (1993) A note on the quality of random variates generated by the ratio of uniforms method. Preprint Series / Department of Applied Statistics and Data Processing, 5. Institut für Statistik und Mathematik, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, Vienna.


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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)

Item Type: Paper
Additional Information: In: ACM Transactions on Modelling and Computer Simulation 4(1), pp. 96-106, 1994
Keywords: ratio of uniforms method / linear congruential generator / discrepancy
Classification Codes: MSC 65C10, CR G.3
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Depositing User: Repository Administrator
Date Deposited: 03 May 2004 20:00
Last Modified: 22 Oct 2019 00:41
URI: https://epub.wu.ac.at/id/eprint/1440


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