April 8, 2013


  • Interesting post on how extreme income inequality is. The distribution is compared to a specific probability model, a ‘power law’, with the distribution of earthquake sizes given as another example. Unfortunately, although the ‘long tail’ point is valid, the ‘power law’ explanation is more dubious.   Earthquake sizes and wealth are two of the large number of empirical examples studied by Aaron Clauset, Cosma Shalizi, and Mark Newman, who find the power law completely fails to fit the distribution of wealth, and is not all that persuasive for earthquake sizes. As Cosma writes

If you use sensible, heavy-tailed alternative distributions, like the log-normal or the Weibull (stretched exponential), you will find that it is often very, very hard to rule them out. In the two dozen data sets we looked at, all chosen because people had claimed they followed power laws, the log-normal’s fit was almost always competitive with the power law, usually insignificantly better and sometimes substantially better. (To repeat a joke: Gauss is not mocked.)



Thomas Lumley (@tslumley) is Professor of Biostatistics at the University of Auckland. His research interests include semiparametric models, survey sampling, statistical computing, foundations of statistics, and whatever methodological problems his medical collaborators come up with. He also blogs at Biased and Inefficient See all posts by Thomas Lumley »