Journal
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 367, Issue 1901, Pages 3281-3296Publisher
ROYAL SOC
DOI: 10.1098/rsta.2009.0075
Keywords
random number; statistical complexity; recurrence plots; excess entropy; rate entropy; permutation entropy
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Funding
- Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Argentina [PIP 5569/04, PIP 5687/05, PIP 6036/05]
- ANPCyT, Argentina [PICT 11-21409/04]
- Universidad Nacional de Mar del Plata
- Australian Research Council (ARC) Centre of Excellence in Bioinformatics, Australia
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We deal with randomness quantifiers and concentrate on their ability to discern the hallmark of chaos in time series used in connection with pseudo-random number generators (PRNGs). Workers in the field are motivated to use chaotic maps for generating PRNGs because of the simplicity of their implementation. Although there exist very efficient general-purpose benchmarks for testing PRNGs, we feel that the analysis provided here sheds additional didactic light on the importance of the main statistical characteristics of a chaotic map, namely (i) its invariant measure and (ii) the mixing constant. This is of help in answering two questions that arise in applications: (i) which is the best PRNG among the available ones? and (ii) if a given PRNG turns out not to be good enough and a randomization procedure must still be applied to it, which is the best applicable randomization procedure? Our answer provides a comparative analysis of several quantifiers advanced in the extant literature.
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