Author:
Zhang Yanfang,Wang Fuchang,Zhao Yibin
Abstract
<abstract><p>Threshold selection is challenging when analyzing tail data with a generalized Pareto distribution. Data below the threshold was not used in the model, resulting in incomplete characterization of the whole data. This paper applied the Gamma distribution, Weibull distribution, and lognormal distribution to fit the central data separately, and a generalized Pareto distribution (GPD) was used to analyze the tail data. In such composite models, the thresholds are estimated directly as parameters. We proposed an empirical distribution function-based parameter estimation method. The absolute value of the difference between the empirical distribution function and the composite distribution function was used as a loss function to obtain an estimate of the parameter. This parameter estimation method is suitable for complex multiparameter distributions. The estimation method based on the empirical distribution function was verified to be feasible through simulation studies. The composite model and the estimation method based on the empirical distribution function were applied to study the earthquake magnitude data to provide a reference for earthquake hazard analysis.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference26 articles.
1. E. Castillo, Extreme value theory in engineering, 1 Eds., New York: Academic Press, 1988. https://doi.org/10.2307/1269867
2. V. F. Pisarenko, A. Sornette, D. Sornette, Characterization of the tail of the distribution of earthquake magnitudes by combining the GEV and GPD descriptions of extreme value theory, Pure Appl. Geophys., 171 (2014), 1599–1624. https://doi.org/10.1007/s00024-014-0882-z
3. S. Coles, An introduction to statistical modeling of extreme values, 1 Eds., Springer Series in Statistics, London: Springer-Verlag, 2001. Available from: https://www.doc88.com/p-9089129087291.html.
4. C. Scarrott, A. Macdonald, A review of extreme value threshold estimation and uncertainty quantification authors, Revstat-Stat. J., 10 (2012), 33–60. https://doi.org/10.1111/j.1467-842X.2012.00658.x
5. P. Embrechts, C. Klüppelberg, T. Mikosch, Modelling extremal events for insurance and finance, New York: Springer, 1997. https://doi.org/10.1007/978-3-642-33483-2