Estimating the Scale Parameter of a Lévy-stable Distribution via the Extreme Value Approach

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• 关键词：Lévy ; stable law ; Extreme values ; Heavy tails ; Hill’s estimator ; Scale parameter estimator
• 刊名：Methodology And Computing In Applied Probability
• 出版年：2007
• 出版时间：December, 2007
• 年：2007
• 卷：9
• 期：4
• 页码：557-572
• 全文大小：412.0 KB

文摘

The characteristic exponent α of a Lévy-stable law S _α (σ, β, μ) was thoroughly studied as the extreme value index of a heavy tailed distribution. For 1 < α < 2, Peng (Statist. Probab. Lett. 52: 255–264, 2001) has proposed, via the extreme value approach, an asymptotically normal estimator for the location parameter μ. In this paper, we derive by the same approach, an estimator for the scale parameter σ and we discuss its limiting behavior.