Pareto Distribution

The Pareto distribution is a probability distribution named after economist Vilfredo Pareto, originally formulated to describe the observation that a small fraction of the population controls a large fraction of the wealth. In its modern form, it is a heavy-tailed distribution in which the probability of observing a value greater than x decreases as a power law, making extreme events far more likely than in normal distributions.

The Pareto distribution appears throughout complex systems: in the distribution of wealth, city sizes, firm revenues, and network degrees. It is the signature of processes governed by cumulative advantage and preferential attachment, and it serves as the statistical fingerprint of systems that amplify initial differences rather than regressing to the mean.