The generalized Box-Müller algorithm provides a methodology for generating q-Gaussian random variates, which generalizes the Gaussian$(q=1)$. The parameter$-\infty < {q}\le 3$is related to the shape of the tail decay;${q} < 1$for compact-support including parabola$\left ({{q}={\it{ 0}} }\right)$;$1 < {q}\le 3$for heavy-tail including Cauchy$\left ({{q}=2 }\right)$. This addendum clarifies the transformation${q}^{\prime }=\frac {3{q}-1}{{q}+1}$within the algorithm is due to a difference in the dimensions d of the generalized logarithm and the generalized distribution. The transformation is clarified by the decomposition of${q}=1+\frac {2\kappa }{1+{d}\kappa }$, where the shape parameter$-1 < \kappa \le \infty $quantifies the magnitude$\vphantom {^{R}}$of the deformation from exponential. A simpler specification for the generalized Box-Müller algorithm is provided using the shape of the tail decay.

The q-Gaussian distribution is known to be an attractor of certain correlated systems and is the distribution which, under appropriate constraints, maximizes a generalization of the familiar Shannon entropy. This generalized entropy, or q-entropy, provides the basis of nonextensive statistical mechanics, a theory which is postulated as a natural extension of the standard (Boltzmann-Gibbs) statistical mechanics, and which 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. 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-Miiller method is developed and presented. This method is suitable for a larger range of q values, -infin < 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.