Concepts and Recent Advances in Generalized Information Measures and Statistics

1. Since the introduction of the information measure widely known as Shannon entropy, quantifiers based on information theory and concepts such as entropic forms and statistical complexities have ...
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Statistical Complexity of Chaotic Pseudorandom Number Generators

Pp. 283-308 (26)

Hilda A. Larrondo, Luciana De Micco, Claudio M. Gonzalez, Angelo Plastino and Osvaldo A. Rosso

Abstract

This chapter deals with the use of the Statistical Complexity Measure, as defined by Lopez Ruiz, Mancini and Calbet [Phys. Lett. A 209 (1995) 321–326] and modified by Rosso and coworkers [P. W. Lamberti, M. T. Martin, A. Plastino, O. A. Rosso; Physica A 334 (2004) 119–131] to characterize pseudo random number generators (PRNG’s) obtained from chaotic dynamical systems. It is shown that two probability distribution functions are required for a proper characterization: the first one is based on the histogram and is used to characterize the uniformity of the values in the time series; the second one is based on the permutation procedure proposed by Bandt and Pompe [Phys. Rev. Lett. 88 (2002) 174102] and characterize the uniformity of patterns of several consecutive values of the time series.

Keywords:

Chaos, Random number generators, Entropy, Statistical Complexity.

Affiliation:

Facultad de Ingenieria, Universidad Nacional de Mar del Plata, Juan B. Justo 4302, 7600 Mar del Plata, Argentina