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Binary decompositions of probability densities and random-bit simulation

Author

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  • Nekrutkin Vladimir

    (St. Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034, Russia)

Abstract

This paper is devoted to random-bit simulation of probability densities, supported on [0,1]{[0,1]}. The term “random-bit” means that the source of randomness for simulation is a sequence of symmetrical Bernoulli trials. In contrast to the pioneer paper [D. E. Knuth and A. C. Yao, The complexity of nonuniform random number generation, Algorithms and Complexity, Academic Press, New York 1976, 357–428], the proposed method demands the knowledge of the probability density under simulation, and not the values of the corresponding distribution function. The method is based on the so-called binary decomposition of the density and comes down to simulation of a special discrete distribution to get several principal bits of output, while further bits of output are produced by “flipping a coin”. The complexity of the method is studied and several examples are presented.

Suggested Citation

  • Nekrutkin Vladimir, 2020. "Binary decompositions of probability densities and random-bit simulation," Monte Carlo Methods and Applications, De Gruyter, vol. 26(2), pages 163-169, June.
    • Handle: RePEc:bpj:mcmeap:v:26:y:2020:i:2:p:163-169:n:5
    DOI: 10.1515/mcma-2020-2063
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