Stable Distributions

12

Sample of size N=10^4

200        400        600        800        1000

Order statistics

50000

100000

Order statistics

Order statistics

Figure 1.5: Plots of the Hill statistics <^_n,_k vs. the maximum order statistic
k for 1.8-stable samples of size N = 10⁴ (top panel) and N = 10⁶
(left and right panels). Red horizontal lines represent the true value
of α. For better exposition, the right panel is a magnification of
the left panel for small k. A close estimate is obtained only for
k = 500,..., 1300 (i.e. for k < 0.13% of sample size).

θ STFstab05.xpl