Indraniel's Notebook

Appreciating Long-Tailed Distributions

29 May 2016

Long-Tailed Distributions (or power-law distributions) are everywhere; they're especially observable in the social sciences, for example:

While these distributions are common, they always feel suprising, and mysterious.

"Despite a century of scientific familiarity, samples drawn from Pareto distributions are routinely presented to the public as anomalies, which prevents us from thinking clearly about the world.

— Clay Shirky from The Guardian

Below is a video I recently encountered explaining them.

I really like this video because of how it gives a very intuitive reason why these distributions arise. Additionally, it also gives an better notion of how a "winners become winners" scheme eventually leads to a power-law distributions.

It's also important to remember that the converse isn't true: observing a power-law doesn't always mean that it was generated by a "winners become winners" scheme. For example, in computer networking, data packet arrival times oven follow a long-tailed distribution, but the packets aren't generated from a "winners become winners" scheme.