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The Gumbel hypothesis test for left censored observations using regional earthquake records as an example

机译：以区域地震记录为例的左删失观测数据的Gumbel假设检验

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Annual maximum (AM) time series are incomplete (i.e., censored) when no events are included above the assumed censoring threshold (i.e., magnitude of completeness). We introduce a distrtibutional hypothesis test for left-censored Gumbel observations based on the probability plot correlation coefficient (PPCC). Critical values of the PPCC hypothesis test statistic are computed from Monte-Carlo simulations and are a function of sample size, censoring level, and significance level. When applied to a global catalog of earthquake observations, the left-censored Gumbel PPCC tests are unable to reject the Gumbel hypothesis for 45 of 46 seismic regions. We apply four different field significance tests for combining individual tests into a collective hypothesis test. None of the field significance tests are able to reject the global hypothesis that AM earthquake magnitudes arise from a Gumbel distribution. Because the field significance levels are not conclusive, we also compute the likelihood that these field significance tests are unable to reject the Gumbel model when the samples arise from a more complex distributional alternative. A power study documents that the censored Gumbel PPCC test is unable to reject some important and viable Generalized Extreme Value (GEV) alternatives. Thus, we cannot rule out the possibility that the global AM earthquake time series could arise from a GEV distribution with a finite upper bound, also known as a reverse Weibull distribution. Our power study also indicates that the binomial and uniform field significance tests are substantially more powerful than the more commonly used Bonferonni and false discovery rate multiple comparison procedures.
机译：如果没有任何事件超出假定的审查阈值（即完整性的大小），则年度最大（AM）时间序列是不完整的（即被审查）。我们基于概率图相关系数（PPCC）为左删截的Gumbel观测值引入了区分假设检验。 PPCC假设检验统计量的关键值是根据蒙特卡洛模拟计算得出的，并且是样本量，审查级别和显着性级别的函数。如果将其应用于全球地震观测目录，则左删截的Gumbel PPCC检验无法拒绝46个地震区域中有45个的Gumbel假设。我们将四种不同的现场显着性检验应用于将单个检验合并为一个整体假设检验。现场意义测试均不能拒绝全球性假设，即AM地震震级是由Gumbel分布引起的。由于字段显着性水平不是决定性的，因此当样本来自更复杂的分布替代方案时，我们还计算了这些字段显着性测试无法拒绝Gumbel模型的可能性。一项电源研究表明，经过审查的Gumbel PPCC测试无法拒绝某些重要且可行的通用极值（GEV）替代方案。因此，我们不能排除全球AM地震时间序列可能来自具有有限上限的GEV分布（也称为反向威布尔分布）的可能性。我们的功效研究还表明，二项式和统一场显着性检验比更常用的Bonferonni和错误发现率多重比较程序强大得多。

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