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

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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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Authors and Affiliations

  1. Laboratory of Applied Mathematics, University Mohamed Khider, P.O. Box 145, 07000, Biskra, Algeria

    Djamel Meraghni & Abdelhakim Necir

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  1. Djamel Meraghni
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  2. Abdelhakim Necir
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Correspondence to Abdelhakim Necir.

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Meraghni, D., Necir, A. Estimating the Scale Parameter of a Lévy-stable Distribution via the Extreme Value Approach. Methodol Comput Appl Probab 9, 557–572 (2007). https://doi.org/10.1007/s11009-007-9021-y

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  • DOI: https://doi.org/10.1007/s11009-007-9021-y

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