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Bootstrap determination of the reliability of b-values: an assessment of statistical estimators with synthetic magnitude series

Abstract : We consider some practical issues of the determination of the b-value of sequences of magnitudes with the bootstrap method for short series of length L and various quantization levels Dm of the magnitude. Preliminary Monte Carlo tests performed with Dm ¼ 0 demonstrate the superiority of the maximum likelihood estimator bMLE, and the inconsistency of the, yet often used, bLR estimator defined as the least-squares slope of the experimental Gutenberg-Richter curve. The Monte Carlo tests are also applied to an estimator, bKS, which minimizes the Kolmogorov-Smirnov distance between the cumulative distribution of magnitudes and a power-law model. Monte Carlo tests of discrete versions of the bMLE and bKS estimators are done for Dm ¼ f0:1; 0:2; 0:3g and used as reference to evaluate the performance of the bootstrap determination of b. We show that all estimators provide b estimates within 10 % error for L C 100 and if a large number, n = 2 9 105, of bootstrapped sample series is used. A resolution test done with Dm ¼ 0:1 reveals that a clear distinction between b = 0.8, 1.0, and 1.2 is obtained if L= 200.
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https://hal-brgm.archives-ouvertes.fr/hal-00779250
Contributeur : Mendy Bengoubou-Valerius <>
Soumis le : lundi 21 janvier 2013 - 21:33:51
Dernière modification le : vendredi 27 mars 2020 - 02:12:36
Archivage à long terme le : : lundi 22 avril 2013 - 04:55:14

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Mendy Bengoubou-Valerius, Dominique Gibert. Bootstrap determination of the reliability of b-values: an assessment of statistical estimators with synthetic magnitude series. Natural Hazards, Springer Verlag, 2013, 65 (1), pp.443-459. ⟨10.1007/s11069-012-0376-1⟩. ⟨hal-00779250⟩

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