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29 March 2024
 
  » arxiv » cond-mat/0605570

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Generalized Box-Muller method for generating q-Gaussian random deviates
William Thistleton ; John A. Marsh ; Kenric Nelson ; Constantino Tsallis ;
Date 23 May 2006
Subject Statistical Mechanics
AbstractThe q-Gaussian distribution is known to be an attractor of certain correlated systems, and is the distribution which, under appropriate constraints, maximizes the entropy Sq, basis of nonextensive statistical mechanics. This theory is postulated as a natural extension of the standard (Boltzmann-Gibbs) statistical mechanics, and may explain the ubiquitous appearance of heavy-tailed distributions in both natural and man-made systems. The q-Gaussian distribution is also used as a numerical tool, for example as a visiting distribution in Generalized Simulated Annealing. We develop and present a simple, easy to implement numerical method for generating random deviates from a q-Gaussian distribution based upon a generalization of the well known Box-Muller method. Our method is suitable for a larger range of q values, q<3, than has previously appeared in the literature, and can generate deviates from q-Gaussian distributions of arbitrary width and center. MATLAB code showing a straightforward implementation is also included.
Source arXiv, cond-mat/0605570
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