Comments on “Generalized Box-Müller Method for Generating q-Gaussian Random Deviates”

The generalized Box-Muller algorithm provides a methodology for generating q-Gaussian random variates, which generalizes the Gaussian $(q=1)$ . The parameter $-\infty is related to the shape of the tail decay; ${q} for compact-support including parabola $\left ({{q}={\it{ 0}} }\right)$ ; $1 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 quantifies the magnitude $\vphantom {^{R}}$ of the deformation from exponential. A simpler specification for the generalized Box-Muller algorithm is provided using the shape of the tail decay.