Disaster risk assessment using mixed extreme value distributions

초록

This paper presents mixed extreme value distributions to assess disaster risk. Various types of mixed distributions are employed for analyzing fatality risk induced by disasters that have affected the United States from 1837 to 2019. Stationary extreme value distribution may not fit the fatality distribution successfully, especially when multiple causes affect extreme outliers in the fatality data. To analyze the risk induced by the disaster, four types of parametric mixture models are investigated; the Weibull-generalized extreme value (GEV) model, the Weibull-generalized Pareto distribution (GPD) model, the GEV-GEV model, and the GEV-GPD model. We estimate parameters by the maximum likelihood (ML) method, except the mixing probability which is estimated by minimizing the integrated absolute errors (IAE), so as to assign more weight to the event in upper tail region. Exceedance frequency (FN) curves constructed from the parametric models are compared on a goodness-of-fit measure based on residuals. The stationary GPD model outperformed others in most criteria except the IAE, but the GPD model did not provide good estimates at high risk levels. The GEV-GEV model and the GEV-GPD model fitted better than other models in the IAE criteria. We constructed confidence bands of the FN-curve for the two models. The confidence interval of the return period for extremely high return level revealed that the GEV-GEV model provides more stable results. The proposed methodology can be applied to other disaster data affected by multiple causes. © ICIC International 2020.

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