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

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.