Power Law Distribution
Within probability, power laws describe an exponential relation between the size of an event and the frequency of its occurrence. Power law distributions result in what is called a long tail graph where there are a few occurrences of an extremely large scale, while there are very many occurrences of a very small scale. These extreme events that are much more likely within power law distributions render our traditional conception of average and normal no longer applicable. Unlike normal distributions in a power law distribution as we increase the number of samples we take values will not converge to an average, they will, in fact, diverge, with some exceptions. Asking for an average is like asking how big is a stone or how long is an average piece of string? It has been empirically proven that many types of systems follow this type of distribution from traffic on the internet to the occurrence of earthquakes and stock market crashes. Power law distributions are a hallmark of nonlinear systems.