I like Cosma's (the author of this piece) point on another of his blog-posts on this topic of whether you've found a power law distribution[1]: Ask yourself wh

I like Cosma's (the author of this piece) point on another of his blog-posts on this topic of whether you've found a power law distribution[1]: Ask yourself whether you really care. Maybe you don't. A lot of the time, we think, all that's genuine important is that the tail is heavy, and it doesn't really matter whether it decays linearly in the log of the variable (power law) or quadratically (log-normal) or something else. But I don't know why I would expect the distribution of library books to be a power law: physical books are inherently limited in how many people can hold them. And the number of books at my school library that are permanently checked out always is rather high. There's a strict upper bound on the max-circulation of a book, so you don't get those super-high values for a few books required to make a power law work. Besides, do you care that it is log-normal and not power? I think the lesson is stop calling things "power law" when you mean "fat-tailed". Fat-tailed is a good enough description in most use-cases anyway. -- [1] http://cscs.umich.edu/~crshalizi/weblog/491.html http://cscs.umich.edu/~crshalizi/weblog/491.html