“…Consider, next, a rescaling of the power law and Fréchet distributions ( > 0) by a positive factor r, This means that the power law distribution and the extreme-value end of the Fréchet distribution are "regularly varying" (e.g., Beirlant et al, 2004, Chapter 2.9.2;Bingham et al, 1987;Zwart, 2009, Chapter 2.1), "scale-invariant," or "self-similar" (e.g., Corral & González, 2019;Ghil et al, 2011;Sornette, 2006)-that is, a scaling of the independent variable x gives a corresponding power scaling of the distribution. In contrast, the lognormal distribution does not have this self-similar property,…”