Estimating 𝐿-Functionals for Heavy-Tailed Distributions and Application

Figure 1

Plots of Hill estimators, as functions of the number of extreme statistics, 𝛼 (solid line), 𝛼_𝑅 (dashed line), and 𝛼_𝐿 (dotted line) of the characteristic exponent 𝛼 of a stable distribution skewed to the right, based on 1000 observations with 50 replications. The horizontal line represents the true value of 𝛼=1.2.