IEICE TRANSACTIONS on Fundamentals
A New Theoretical Test for Pseudorandom Number Generators Which Is Based on Perron-Frobenius Operator
Summary :
A new statistical test has been recently presented for determining whether a binary sequence into which a real-valued sequence to be tested is transformed precisely mimics Bernoulli trials B (p, q) with probabilities of 0 and of 1, p and q, or not. This paper gives a theoretical test based on such a stringent test and shows its usefulness. This method uses the ensemble average technique under the assumption that the pseudorandom-number generator is mixing with respect to an absolutely continuous measure. The existence of such a measure permits us to theoretically calculate the ensemble average of several statistics by using the Perron-Frobenius integral operator. Furthermore, this operator releases us from cumbersome and tedious procedures to calculate multivariate distributions, in connection with several statistical tests. Three kinds of tests, the runs test, poker test, and serial correlation test are presented. The Galerkin approximation to the operator on a suitable functional space is also introduced which provides a finite dimensional matrix (referred to as a Galerkin-approximated matrix of the Perron-Frobenius operator). The largest eigenvalue of the matrix, nearly equal to 1, corresponds to the existence of the measure. Each theoretical value of three tests for B (p, q) shows that the magnitude of the second largest eigenvalue plays an important role in determing randomness of the sequence generated by the generation.
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- IEICE TRANSACTIONS on Fundamentals Vol.E74-A No.6 pp.1430-1436
- Publication Date
- 1991/06/25
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- Special Section PAPER (Special Issue on Nonlinear Theory and Its Applications)
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Tohru KOHDA, "A New Theoretical Test for Pseudorandom Number Generators Which Is Based on Perron-Frobenius Operator" in IEICE TRANSACTIONS on Fundamentals,
vol. E74-A, no. 6, pp. 1430-1436, June 1991, doi: .
Abstract: A new statistical test has been recently presented for determining whether a binary sequence into which a real-valued sequence to be tested is transformed precisely mimics Bernoulli trials B (p, q) with probabilities of 0 and of 1, p and q, or not. This paper gives a theoretical test based on such a stringent test and shows its usefulness. This method uses the ensemble average technique under the assumption that the pseudorandom-number generator is mixing with respect to an absolutely continuous measure. The existence of such a measure permits us to theoretically calculate the ensemble average of several statistics by using the Perron-Frobenius integral operator. Furthermore, this operator releases us from cumbersome and tedious procedures to calculate multivariate distributions, in connection with several statistical tests. Three kinds of tests, the runs test, poker test, and serial correlation test are presented. The Galerkin approximation to the operator on a suitable functional space is also introduced which provides a finite dimensional matrix (referred to as a Galerkin-approximated matrix of the Perron-Frobenius operator). The largest eigenvalue of the matrix, nearly equal to 1, corresponds to the existence of the measure. Each theoretical value of three tests for B (p, q) shows that the magnitude of the second largest eigenvalue plays an important role in determing randomness of the sequence generated by the generation.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e74-a_6_1430/_p
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@ARTICLE{e74-a_6_1430,
author={Tohru KOHDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A New Theoretical Test for Pseudorandom Number Generators Which Is Based on Perron-Frobenius Operator},
year={1991},
volume={E74-A},
number={6},
pages={1430-1436},
abstract={A new statistical test has been recently presented for determining whether a binary sequence into which a real-valued sequence to be tested is transformed precisely mimics Bernoulli trials B (p, q) with probabilities of 0 and of 1, p and q, or not. This paper gives a theoretical test based on such a stringent test and shows its usefulness. This method uses the ensemble average technique under the assumption that the pseudorandom-number generator is mixing with respect to an absolutely continuous measure. The existence of such a measure permits us to theoretically calculate the ensemble average of several statistics by using the Perron-Frobenius integral operator. Furthermore, this operator releases us from cumbersome and tedious procedures to calculate multivariate distributions, in connection with several statistical tests. Three kinds of tests, the runs test, poker test, and serial correlation test are presented. The Galerkin approximation to the operator on a suitable functional space is also introduced which provides a finite dimensional matrix (referred to as a Galerkin-approximated matrix of the Perron-Frobenius operator). The largest eigenvalue of the matrix, nearly equal to 1, corresponds to the existence of the measure. Each theoretical value of three tests for B (p, q) shows that the magnitude of the second largest eigenvalue plays an important role in determing randomness of the sequence generated by the generation.},
keywords={},
doi={},
ISSN={},
month={June},}
Copy
TY - JOUR
TI - A New Theoretical Test for Pseudorandom Number Generators Which Is Based on Perron-Frobenius Operator
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1430
EP - 1436
AU - Tohru KOHDA
PY - 1991
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E74-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 1991
AB - A new statistical test has been recently presented for determining whether a binary sequence into which a real-valued sequence to be tested is transformed precisely mimics Bernoulli trials B (p, q) with probabilities of 0 and of 1, p and q, or not. This paper gives a theoretical test based on such a stringent test and shows its usefulness. This method uses the ensemble average technique under the assumption that the pseudorandom-number generator is mixing with respect to an absolutely continuous measure. The existence of such a measure permits us to theoretically calculate the ensemble average of several statistics by using the Perron-Frobenius integral operator. Furthermore, this operator releases us from cumbersome and tedious procedures to calculate multivariate distributions, in connection with several statistical tests. Three kinds of tests, the runs test, poker test, and serial correlation test are presented. The Galerkin approximation to the operator on a suitable functional space is also introduced which provides a finite dimensional matrix (referred to as a Galerkin-approximated matrix of the Perron-Frobenius operator). The largest eigenvalue of the matrix, nearly equal to 1, corresponds to the existence of the measure. Each theoretical value of three tests for B (p, q) shows that the magnitude of the second largest eigenvalue plays an important role in determing randomness of the sequence generated by the generation.
ER -
English
