Journal of Probability and Statistics / 2010 / Article / Fig 1

Research Article

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

Figure 1

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 stable distribution skewed to the right, based on 1 0 0 0 observations with 5 0 replications. The horizontal line represents the true value of ๐›ผ = 1 . 2 .
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