Statistics of Extremes: Animation 1
Abstract
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 an −1 (Zn − bn ) for appropriate sequences an > 0 and bn . In each case, Zn is asymptotically degenerate, whereas an −1 (Zn − bn ) is not.
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