Statistics of Extremes: Animation 5

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 in the bivariate framework for increasing n. The upper left panel displays bivariate Student t data with 2 degrees of freedom and standard Pareto marginals, rescaled by n. These data are asymptotically dependent. The right-hand panels show the corresponding histograms of the pseudoradius R and pseudoangle W for points lying above the threshold defined by R > 10⁻² (solid blue line), with limiting densities superimposed in red. The bottom plots illustrate the Gaussian case, which is asymptotically independent; here the limiting distribution of W places equal point masses of .5 at w = 0 and w = 1, and it has no mass elsewhere.