The scrambles of halton sequence and thier weaknesses

Document Type : Research Paper

Authors

1 Department of Statistics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

2 Department of Statistics, Science and Research branch, IAU Tehran, Iran

Abstract

So far, many scrambles have been introduced to break the correlation between Halton’s sequence points and improve its
two-dimensional designs. In this paper, some of the most important scrambles that are available to scrambling the Halton sequence are evaluated, and describe their weaknesses. Also, we introduce a new method that, despite it’s simplicity of execution, has good twodimensional designs.

Keywords

References

[1] Chi, H., Mascagni, M., Warnock, T., On the Optimal halton Sequences, Math. Comput. in Simul., 70(1) (2005), 9-21.
[2] Fathi Vajargah, B., Eskandari Chechaglou, A., Optimal halton sequence via inversive Scrambling, Communications in Statistics Simulation and Computation, 42 (2013), 476-484.
[3] Vandewoestyne, B., Quasi-Monte Carlo techniques for the approximation of highdimensional integrals, [PhD theses] Advisor Ronald Cools,June 2008.
[4] M. Mascagni, H. Chi, On the scrambled Halton sequences, Monte Carlo Meth. Appl., 10 (2013), 435-442.
Journal of Hyperstructures
Volume 9, Issue 1
June 2020
Pages 40-53

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