Pareto distribution

The Pareto distribution is a probability distribution named after Vilfredo Pareto. It is continuous and follows a power law. It is a heavy tailed distribution. The Pareto distribution was first used to show how income is distributed among households (which is commonly called Income distribution). Pareto distributions are often used in the cases when many different small independent factors contribute to a result. Pareto wrote a book called Cours d'économie politique, where he tried to show that the number of people who have an income greater than x is proportional to ${\displaystyle 1/x^{k}}$. The parameter ${\displaystyle k}$ is constant, and about 1.5. This is all that is needed to describe the Pareto distribution. Insurance companies often use Pareto distributions to model damage.

Beyond its historical roots in economics, the Pareto distribution^[1] has become an essential analytical tool across numerous disciplines because it accurately captures the behavior of complex systems. For instance, in the insurance sector, firms utilize this distribution to assess the probability of rare but catastrophic claims, as standard statistical models often underestimate the likelihood of such extreme events. By focusing on the power-law nature of these occurrences, analysts can better prepare for the outsized impact that a tiny percentage of events often the most severe ones can have on total financial exposure.

1. ↑ "Pareto Distribution: A Comprehensive Guide". www.datacamp.com. Retrieved 2026-05-26.