Power law distributions are observed in numerous real world and natural phenomena in the fields of physics, biology, sociology and linguistics. Think of the 80-20 rule which was discovered by the an Italian economist Pareto who observed that 80% of the wealth is distributed among 20% of the population.
I came across a non-intuitive example of such a distribution.
Think of your behavior on the phone – are most of your calls short or long or are they distributed normally around an average length. I was expecting to see a Gaussian bell shaped distribution but to my surprise it turns out that we have a lot of short calls and few long ones.
I have access to some data around call length information for calls random people make to yellow page advertisers. Here is data from one random advertiser with random call samples and guess what – it looks like a power-law distribution.