What is Extreme-value theory, GEV distribution?

Extreme-value theory studies the laws of maxima and of exceedances of high thresholds. The generalised extreme value distribution with shape $\xi$ has distribution function $G_\xi(x) = \exp\bigl(-(1 + \xi x)^{-1/\xi}\bigr)$ for $1 + \xi x > 0$ (and $\exp(-e^{-x})$ for $\xi = 0$), up to location and scale.