Statistics of Extremes: Animation 2

An animation from the 2015 review by A.C. Davison and R. Huser, "Statistics of Extremes," from the Annual Review of Statistics and Its Application.

Illustration of the point process of exceedances and the convergence to the GPD. For increasing values of n, the plots display the point process of rescaled times and rescaled variables, namely (j/(n + 1), (Y_j − b_n )/a_n ), for data simulated from the uniform (top left), standard Gaussian (top right), unit exponential (bottom left), and 0.2-Pareto distributions. The side plots are histograms of the exceedances over the threshold u (horizontal blue line), i.e., a_n ⁻¹(Y_j − b_n )|a_n ⁻¹(Y_j − b_n ) > u. The solid red curves are the corresponding asymptotic GPD densities.