Long-Tailed Distributions (or power-law distributions) are everywhere; they're especially observable in the social sciences, for example:
- Wealth Distribution: a select few people control most of the wealth
- Social Media and Networks: famous people have thousands of times more followers than the average user.
- Market Dominance: Amazon is much larger than the next few internet retailers by revenue
- Internet Infrastructure: many DevOps and computer infrastructure related issues have long tails
"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.