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Recurrence Plots as an Exploratory Graphical Tool for Evaluating Randomness

난수의 임의성을 평가하기 위한 탐색적 그림도구로서의 재현그림

  • Jang, Dae-Heung (Division of Mathematical Sciences, Pukyong National University)
  • 장대흥 (부경대학교 수리과학부 통계학)
  • Received : 20090700
  • Accepted : 20091000
  • Published : 2009.12.31

Abstract

There are many traditional statistical tests for randomness. We can consider recurrence plots as an exploratory graphical tool for evaluating randomness.

의사난수발생기로부터 얻어지는 난수의 임의성을 검정하기 위한 통계방법들이 기존에 많이 제시되었다. 수열의 임의성을 평가하기 위한 탐색적 그림도구로서 우리는 재현그림을 이용할 수 있다.

Keywords

References

  1. 장대흥 (2002). 탐색적 자료분석시 그래프의 활용에 대한 연구, <응용통계연구>, 15, 433–448
  2. Castro, J. C. H., Sierra, J. M., Seznec, A., Izquierdo, A. and Ribagorda, A. (2005). The strict avalanche criterion randomness test, Mathematics and Computers in Simulation, 68, 1–7 https://doi.org/10.1016/j.matcom.2004.09.001
  3. Chatterjee, S., Yilmaz, M., Habibullah, M. and Laudato, M. (2000). An approximate entropy test for randomness, Communications in Statistics-Theory and Methods, 29, 655–675 https://doi.org/10.1080/03610920008832508
  4. Eckmann, J. P., Kamphorst, S. O. and Ruelle, D. (1987). Recurrence plots of dynamical systems, Europhysics Letters, 5, 973–977
  5. Hamano, K. and Kaneko, T. (2007). Correction of overlapping template matching test included in NIST randomness test suite, IEICE Transaction on Fundamentals of Electronics, Communications and Com-puter Sciences, E90-A, 1788–1792
  6. Hamano, K. and Yamamoto, H. (2008). A randomness test based on T-codes, Proceedings in International Symposium on Information Theory and its Applications, 2008
  7. Katos, V. (2005). A randomness test for block ciphers, Applied Mathematics and Computation, 162, 29–35 https://doi.org/10.1016/j.amc.2003.12.122
  8. Kim, C., Choe, G. H. and Kim, D. H. (2008). Tests of randomness by the gambler's ruin algorithm, Applied Mathematics and Computation, 199, 195–210 https://doi.org/10.1016/j.amc.2007.09.060
  9. Marsaglia, G. and Tsang, W. W. (2002). Some difficult-to-pass tests of randomness, Journal of Statistical Software, 7, 3
  10. Marwan, N., Romano, M. C., Thiel, M. and Kurths, J. (2007). Recurrence plots for the analysis of complex systems, Physics Reports, 438, 237–329 https://doi.org/10.1016/j.physrep.2006.11.001
  11. Matassini, L., Kantz, H., Holyst, J. and Hegger, R. (2002). Optimizing of recurrence plots for noise reduction, Physical Review E, 65, 021102 https://doi.org/10.1103/PhysRevE.65.021102
  12. Mindlin, G. M. and Gilmore, R. (1992). Topological analysis and synthesis of chaotic time series, Physica D, 58, 229–242 https://doi.org/10.1016/0167-2789(92)90111-Y
  13. Rukhin, A. L. and Volkovich, Z. (2008). Testing randomness via aperiodic words, Journal of Statistical Computation and Simulation, 78, 1133–1144 https://doi.org/10.1080/10629360600864142
  14. Ryabko, B. Y. and Monarev, V. A. (2005). Using information theory approach to randomness testing, Journal of Statistical Planning and Inference, 133, 95–110
  15. Ryabko, B. Y., Stognienko, V. S. and Shokin, Y. I.(2004). A new test for randomness and its application to some cryptographic problem, Journal of Statistical Planning and Inference, 123, 365–376 https://doi.org/10.1016/S0378-3758(03)00149-6
  16. Tan, S. K. and Guan, S. (2009). Randomness quality of permuted pseudorandom binary sequence, Mathe-matics and Computers in Simulation, 79, 1618–1626 https://doi.org/10.1016/j.matcom.2008.07.012
  17. Thiel, M., Romano, M. C., Kurths, J.,. Meucci, R., Allaria, E. and Arecchi, F. T. (2002). Influence of observational noise on the recurrence quantification analysis, Physica D, 171, 138–152
  18. Wang, K., Pei, W., Xia, h. and Cheung. Y. (2008). Pseudo-Random number generator based on asymptotic deterministic randomness, Physics Letters A, 372, 4388–4394 https://doi.org/10.1016/j.physleta.2008.04.002
  19. Zbilut, J. P. and Webber Jr., C. L. (1992). Embeddings and delays as derived from quantification of recurrence plots, Physics Letters A, 171, 199–203 https://doi.org/10.1016/0375-9601(92)90426-M
  20. Zbilut, J. P., Zaldivar-Commenges, J. M. and Strozzi, F. (2002). Recurrence quantification based Liapunov exponents for monitoring divergence in experimental data, Physics Letters A, 297, 173–181 https://doi.org/10.1016/S0375-9601(02)00436-X

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