Chaotic Method for Generating q-Gaussian Random Variables

Author

Umeno, Ken ; Sato, Akira

Author_Institution

Dept. of Appl. Math. & Phys., Kyoto Univ., Kyoto, Japan

Volume

59

Issue

5

fYear

2013

fDate

May-13

Firstpage

3199

Lastpage

3209

Abstract

This study proposes a pseudorandom number generator of q -Gaussian random variables for a range of q values, -∞ <; q <; 3, based on deterministic chaotic map dynamics. Our method consists of chaotic maps on the unit circle and map dynamics based on the piecewise linear map. We perform the q-Gaussian random number generator for several values of q and conduct both Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) tests. The q-Gaussian samples generated by our proposed method pass the KS test at more than 5% significance level for values of q ranging from -1.0 to 2.7, while they pass the AD test at more than 5% significance level for q ranging from -1 to 2.4.

Keywords

Gaussian distribution; random number generation; AD tests; Anderson-Darling tests; KS tests; Kolmogorov-Smirnov tests; deterministic chaotic map dynamics; piecewise linear map; pseudorandom number generator; q-Gaussian random variables; unit circle; Chebyshev approximation; Density measurement; Distance measurement; Joints; Polynomials; Random variables; $q$-Gaussian distribution; Chebyshev polynomials; ergodic theory; map dynamics; pseudorandom number generator;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2013.2241174

Filename

6414629