An Introduction to Complex Systems Science and Its Applications

Figure 7

A normal distribution (thin-tailed) and a distribution with a power-law decay (fat-tailed). The fat-tailed distribution may appear more stable, due to the lower probability of small-scale fluctuations and the fact that samples from the distribution may not contain any extreme events. However, sooner or later, a fat-tailed distribution will produce an extreme event, while one could wait thousands of lifetimes of the universe before a normal distribution produces a similarly extreme event. Note that the axes of this graph are truncated; the illustrated fat-tailed distribution can, with small but nonnegligible probability (0.04%), produce events with a scale of one million or more.