Power-law distributions seem to be everywhere, and not just in word-counts and whale whistles. Most people know that Vilfredo Pareto found them in the distribution of wealth, two or three decades before Udny Yule showed that stochastic processes like those in evolution lead to such distributions, and George Kingsley Zipf found his eponymous law in word frequencies. Since then, power-law distributions have been found all over the place

Or maybe not? Many of the alleged “power-law” examples are actually log-normal, or some other heavy-tailed distribution, according to a paper by Aaron Clauset, Cosma Rohilla Shalizi, and M. E. J. Newman, “Power-law distributions in empirical data” (SIAM Review 2009). As an alternative to the paper, you can read Cosma’s blog post “So You Think You Have a Power Law — Well Isn’t That Special?”, 6/15/2007; or this summary of the results in “Cozy Catastrophes”, 2/15/2012: