Approximate entropy for testing randomness

Journal of Applied Probability

Volumn 37, Issue 1, 2000, Pages 88-100

  Rukhin, Andrew L ^a,b  

^a UNIVERSITY OF MARYLAND   (United States)

^b UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

Author keywords

Approximate entropy; Distribution of m patterns; Entropy; Information divergence; Serial test; Tail probabilities; 2 distribution

Indexed keywords

EID: 0034341923     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1014842270     Document Type: Article

References (21)

1. BILLINGSLEY, P. (1956). Asymptotic distributions of two goodness of fit criteria. Ann. Math. Statist. 27,1123-1129.
2. CHAITIN, G. (1975). Randomness and mathematical proof. Scientific American 232, 47-52.
3. DEVROYE, L., Gyorfi, L. and Lugosi, G. (1996). A Probabilistic Theory of Pattern Recognition. Springer, New York, pp. 31-34.
4. GOOD, I. J. (1953). The serial test for sampling numbers and other tests for randomness. Proc. Camb. Phil. Soc. 47, 276-284.
5. Good, I. J. (1957). On the serial test for random sequences. Ann. Math. Statist. 28, 262-264.
6. GOOD, I. J. (1997). The roughness of visitations in a Markov chain, a review with extensions. In Advances in the Theory and Practice of Statistics, eds. N. L. Johnson and N. Balakrishnan. John Wiley, New York, pp. 67-87.
7. Good, I. J. and Gover, T. N. (1967). The generalized serial test and the binary expansion of -s/l. J. Roy. Statist. Soc. 130 A, 102-107.
8. Gustafson, H., Dawson, E., Nielsen, L. and Caelli, W. (1994). A computer package for measuring the strength of encryption algorithms. Computers and Security 13, 687-697.
9. KIMBERLEY, M. (1987). Comparison of two statistical tests for keystream sequences. Electron. Lett. 23, 365-366.
10. KNUTH, D. E. (1998). TheArtofComputerProgramming, Vol 2, 3rd edn. Addison-Wesley, Reading, MA, pp. 61-80.
11. MARSAGLIA, G. (1985). A current view of random number generation. In Computer Science and Statistics: Proceedings of the Sixteenth Symposiumon the Interface, Elsevier, New York, pp. 3-10.
12. MARSAGLIA, G. (1996). Diehard: a battery oftestsfor randomness. Available at http://stat.fsu.edu/geo/diehard.html.
13. Menezes, A. J., van Oorschot, P. C. and Vanstone, S. A. (1997). HandbookofApplied Cryptography. CRC Press, Boca Raton, p. 181.
14. MORALES, D., Pardo, L. and Vajda, I. (1996). Uncertainty of discrete stochastic systems: General theory and statistical inference. IEEE Trans. Systems, Man and Cybernetics Part A 26, 681-697.
15. Pincus, S. and Huang, W.-M. (1992). Approximate entropy, statistical properties and applications. Commun. Statist. Part A Theory and Methods 21, 3061-3077.
16. Pincus, S. and Kalman, R. E. (1997). Not all (possibly) ‘random’ sequences are created equal. Proc. Nat. Acad. Sci. USA 94,3513-3518.
17. PINCUS, S. and Singer, B. H. (1996). Randomness and degrees of irregularity. Proc. Nat. Acad. Sci. USA 93, 2083-2088.
18. Rao, C. R. and Mitra, C. K. (1971). GeneralizedInverse ofMatricesand its Applications. John Wiley, New York, pp. 171-173.
19. Read, T. R. and Cressie, N. A. (1988). Goodness-of-FitStatistics for Discrete Multivariate Data. Springer, New York, p. 46.
20. SEIFE, C. (1997). New test sizes up randomness. Science 276, 532.
21. Vajda, I. (1989). Theory ofStatistical Inference and Information. Kluwer, Dordrecht, pp. 300-328.