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A mixture of exponentials distribution for a simple and precise assessment of the volcanic hazard

机译：对幂态分布的混合物，对火山危害的简单和精确评估

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The assessment of volcanic hazard is the first step for disaster mitigation. The distribution of repose periods between eruptions provides important information about the probability of new eruptions occurring within given time intervals. The quality of the probability estimate, i.e., of the hazard assessment, depends on the capacity of the chosen statistical model to describe the actual distribution of the repose times. In this work, we use a mixture of exponentials distribution, namely the sum of exponential distributions characterized by the different eruption occurrence rates that may be recognized inspecting the cumulative number of eruptions with time in specific VEI (Volcanic Explosivity Index) categories. The most striking property of an exponential mixture density is that the shape of the density function is flexible in a way similar to the frequently used Weibull distribution, matching long-tailed distributions and allowing clustering and time dependence of the eruption sequence, with distribution parameters that can be readily obtained from the observed occurrence rates. Thus, the mixture of exponentials turns out to be more precise and much easier to apply than the Weibull distribution. We recommended the use of a mixture of exponentials distribution when regimes with well-defined eruption rates can be identified in the cumulative series of events. As an example, we apply the mixture of exponential distributions to the repose-time sequences between explosive eruptions of the Colima and Popocatépetl volcanoes, México, and compare the results obtained with the Weibull and other distributions.
机译：火山危害评估是减灾的第一步。爆发之间的休息期的分布提供了关于在给定时间间隔内发生的新爆发的概率的重要信息。概率估计的质量，即危险评估，取决于所选择的统计模型的能力来描述休息时间的实际分布。在这项工作中，我们使用指数分布的混合物，即具有不同喷发发生率的指数分布的总和可以被认可检查特定VEI（火山爆炸性指数）类别的时间累积爆发的累积次序。指数混合密度最引人注目的性质是密度函数的形状以类似于经常使用的威布尔分布，匹配长尾分布并允许喷发序列的聚类和时间依赖性的方式灵活，具有分布参数可以从观察到的发生率中容易地获得。因此，指数的混合物变成更精确，更容易施加而不是威布尔分布。我们建议在累计系列事件中确定具有明确定义的喷发率的制度时使用指数分布的混合物。作为一个例子，我们将指数分布的混合物应用于Colima和Pococatépetl火山，México的爆炸性喷发之间的休息时间序列，并比较了用Weibull和其他分布获得的结果。

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