Wat is Generalised Pareto distribution, peaks over threshold?

The generalised Pareto distribution with shape $\xi$ and scale $\beta$ has $\P(Y > y) = (1 + \xi y/\beta)^{-1/\xi}$ for $y \ge 0$ (and $e^{-y/\beta}$ for $\xi = 0$). The peaks-over-threshold method fits it by maximum likelihood to the excesses $X - u$ of the observations above a high threshold $u$.