Understanding the power law and black swan

In this last section, I want to give you a brief overview of the so-called power law and black swan events.

The ubiquitous power law

What is the power law? If you have two quantities such that one varies according to a power relationship of another, and independent of the initial sizes, then you have a power law relationship. Many distributions have a power law shape, rather than normal distributions: . The exponential distribution we saw previously is one such example.

For a real-word example, the frequency of words in most languages follows a power law. The English letter frequencies also roughly follow a power law. e appears the most often, with a frequency of 11%. The following graph taken from Wikipedia (https://en.wikipedia.org/wiki/Letter_frequency) shows a typical example of such a power law:

Figure 5.11 – Frequency of English letters

What's amazing about a power law is not only its universality...