Statistics of Extremes: Animation 1

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 Extremal Types Theorem. For increasing values of n, the left panels display the distribution of the maximum Z _n of n independent uniform (top row), standard Gaussian (second row), unit exponential (third row), and 0.2-Pareto (bottom row), i.e., F(y) = 1 − y ^−0.2, y >  1, random variables. The right panels display the distribution of a_n ⁻¹ (Z_n − b_n ) for appropriate sequences a_n > 0 and b_n . In each case, Z_n is asymptotically degenerate, whereas a_n ⁻¹ (Z_n − b_n ) is not.