Has anyone checked the underlying assumption (that the there’s a power law involved)? My belief was that most long tailed distributions don’t actually follow a power law.
Probably a year or more ago I compared some data on FOIA request processing times reported by US government agencies against an exponential distribution (not power law). I used the given mean and compared the predicted median against the actual median. Was acceptable as far as I was concerned, though I'd have to redo the analysis to actually get quantitative.
With a power law there's no mean or median starting at t = 0, so this sort of comparison isn't possible given the FOIA request data available. I'd be interested in seeing the data on the tails to see if those are power law distributed.
