Generation of quasi-normal variables using discrete chaotic maps

Benjamin C. Flores; Berenice Verdin; Gabriel Thomas; Ali Ashtari

doi:10.1117/12.603962

16 May 2005 Generation of quasi-normal variables using discrete chaotic maps

Benjamin C. Flores, Berenice Verdin, Gabriel Thomas, Ali Ashtari

Proceedings Volume 5788, Radar Sensor Technology IX; (2005) https://doi.org/10.1117/12.603962
Event: Defense and Security, 2005, Orlando, Florida, United States

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.

Citation Download Citation

Benjamin C. Flores, Berenice Verdin, Gabriel Thomas, and Ali Ashtari "Generation of quasi-normal variables using discrete chaotic maps", Proc. SPIE 5788, Radar Sensor Technology IX, (16 May 2005); https://doi.org/10.1117/12.603962

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