Estimating the Scale Parameter of a Lévy-stable Distribution via the Extreme Value Approach |
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Authors: | Djamel Meraghni Abdelhakim Necir |
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Affiliation: | (1) Laboratory of Applied Mathematics, University Mohamed Khider, P.O. Box 145, 07000 Biskra, Algeria |
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Abstract: | 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. |
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Keywords: | Lévy-stable law Extreme values Heavy tails Hill’ s estimator Scale parameter estimator |
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