Before we get carried away with a wave of “power-laws here there and everywhere!” craziness, we have to stop and test our conjectures. Here’s one paper that tests a large number of conjectures: Power-law distributions in empirical data

Sometimes the data tricks you by creating an illusion of a power-law distribution. This could be the result of incomplete or biased samples, or different mechanisms which produce something that superficially looks like an self-organized power-law but is just random.

This study tests how well power-laws fit to the frequency of word use, metabolism, book sales, wealth, internet, earthquakes, blackouts, terrorism and war, and quite a few others. Some fall under discrete or continuous power-laws and they accounted for this.

Things like web-links, fires, earthquakes show moderate support for power-laws with upper and lower cut-offs. There is also moderate support for terrorism and war casualty power-laws. Some things, like word frequency usage follow power-laws almost perfectly. Others – metabolics – do not conform to power-laws.

Terrorism does have a stronger fit than war, but this could just be because of more accurate data. The war sample is relatively small, inaccurate, and casualty counts are always biased.

Here’s the companion website for the journal article. That’s if you’re really boring (like me) and want to play around with datasets and fitting power-law distributions.

Advertisements