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Proceedings Paper

Generation of quasi-normal variables using discrete chaotic maps
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Paper Abstract

We evaluated two random number generator algorithms using first-order and second-order chaotic maps. The first algorithm, which is based on the central limit theorem, allows us to approximate a Gaussian random variable as the sum of a given chaotic sequence. We considered two first-order maps (Bernoulli, Tent) and two second-order maps (Logistic, and Quadratic). In each instance, we verified that the sequence of random numbers had kurtosis of 3. In the case of the Bernoulli map, we determined that the statistical independence of samples is dependent on the map parameter B. The second algorithm, which is based on Von Neumann's Method, allowed us to reject samples from a chaotic sequence with uniform distribution to obtain a Gaussian distribution within a specific range (U, V). For the first-order maps, we estimated their probability density function in this range and computed deviations from the theoretical Gaussian density. In summary, we determined that samples generated via these two algorithms satisfied statistical tests for normal distributions, thus demonstrating that chaotic maps can be effectively to generate Gaussian samples.

Paper Details

Date Published: 16 May 2005
PDF: 8 pages
Proc. SPIE 5788, Radar Sensor Technology IX, (16 May 2005); doi: 10.1117/12.603962
Show Author Affiliations
Benjamin C. Flores, Univ. of Texas at El Paso (United States)
Berenice Verdin, Univ. of Texas at El Paso (United States)
Gabriel Thomas, The Univ. of Manitoba, Winnipeg (Canada)
Ali Ashtari, The Univ. of Manitoba, Winnipeg (Canada)

Published in SPIE Proceedings Vol. 5788:
Radar Sensor Technology IX
Robert N. Trebits; James L. Kurtz, Editor(s)

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