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The acceptance-rejection method for low-discrepancy sequences

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  • Nguyen Nguyet

    (Department of Mathematics and Statistics, Youngstown State University, Youngstown, OH 44555-7994, USA)

  • Ökten Giray

    (Department of Mathematics, Florida State University, Tallahassee FL 32306-4510, USA)

Abstract

Generation of pseudorandom numbers from different probability distributions has been studied extensively in the Monte Carlo simulation literature. Two standard generation techniques are the acceptance-rejection and inverse transformation methods. An alternative approach to Monte Carlo simulation is the quasi-Monte Carlo method, which uses low-discrepancy sequences, instead of pseudorandom numbers, in simulation. Low-discrepancy sequences from different distributions can be obtained by the inverse transformation method, just like for pseudorandom numbers. In this paper, we present an acceptance-rejection algorithm for low-discrepancy sequences. We prove a convergence result, and present error bounds. We then use this acceptance-rejection algorithm to develop quasi-Monte Carlo versions of some well-known algorithms to generate beta and gamma distributions, and investigate the efficiency of these algorithms numerically. We also consider the simulation of the variance gamma model, a model used in computational finance, where the generation of these probability distributions are needed. Our results show that the acceptance-rejection technique can result in significant improvements in computing time over the inverse transformation method in the context of low-discrepancy sequences.

Suggested Citation

  • Nguyen Nguyet & Ökten Giray, 2016. "The acceptance-rejection method for low-discrepancy sequences," Monte Carlo Methods and Applications, De Gruyter, vol. 22(2), pages 133-148, June.
    • Handle: RePEc:bpj:mcmeap:v:22:y:2016:i:2:p:133-148:n:1
    DOI: 10.1515/mcma-2016-0104
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    References listed on IDEAS

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