Probability distributions

Some probability distributions that are useful (usually to economists) for one reason or another.

Pareto Distribution

The Pareto distribution has a simple CDF: $G(x) = 1 - \underline{x}^{\gamma}x^{-\gamma}$, where $\underline{x}$ satisfies $G(\underline{x}) = 0$ and $\gamma$ governs the variance.

A useful property of the Pareto distribution is that when it is truncated, the truncated CDF is the same as the original, except that $\underline{x}$ is moved up.