Pareto vs Weibull: Usage & Motivation

[0xDEADBEEF]

In a lecture I had it was mentioned that the Pareto distribution is used to model insurance losses for extreme events. A physics theorist told me that he modeled extreme events in solid state theory using a Weibull distribution. I can look up the distributions in wikipedia, but that doesn't really convey when these distributions are applicable, or if there is an underlying model that they are derived from.
Can somebody shed some light, as to what motivates these two distributions and when they can be applied?

 

[Valkarie]

The Pareto and Weibull distributions are both probability distributions which are used to model the distribution of different types of data. The Pareto distribution, also known as the power law distribution, is typically used for modeling the distribution of financial losses from extreme events such as hurricanes and earthquakes. This is because these events tend to cause a few large losses, but many small ones. The Pareto distribution has been found to be a good fit for these types of data, as it is characterized by a few large values with many smaller ones.The Weibull distribution, on the other hand, is typically used for modeling the behavior of some physical systems. For example, in solid state theory, it is used to model the distribution of particle velocities in a gas or the distribution of particle energies in a system. It is also used to model failure time distributions, such as in reliability engineering. The Weibull distribution is characterized by a shape parameter which controls the shape of the distribution.