Journal of Probability and Statistics / 2010 / Article / Fig 3

Research Article

Estimating ๐ฟ -Functionals for Heavy-Tailed Distributions and Application

Figure 3

Plots of Hill estimators, as functions of the number of extreme statistics, ๎ ๐›ผ (solid line), ๎ ๐›ผ ๐‘… (dashed line) and ๎ ๐›ผ ๐ฟ (dotted line) of the characteristic exponent ๐›ผ of a symmetric stable distribution, based on 1 0 0 0 observations with 5 0 replications. The horizontal line represents the true value of ๐›ผ = 1 . 2 .
707146.fig.003