Abstract In many complex systems studied in statistical physics, inter-arrival times between events such as solar flares, trades and neuron voltages follow a heavy-tailed distribution. The set of event times is fractal-like, being dense in some time windows and empty in others, a phenomenon which has been dubbed “bursty”. A new model for the inter-exceedance times of such events above high thresholds is proposed. For high thresholds and infinite-mean waiting times, it is shown that the times between threshold crossings are Mittag-Leffler distributed, and thus form a “fractional Poisson Process” which generalizes the standard Poisson Process of threshold exceedances. Graphical means of estimating model parameters and assessing model fit are provided. The inference method is applied to an empirical bursty time series, and it is shown how the memory of the Mittag-Leffler distribution affects prediction of the time until the next extreme event.

中文翻译：

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突发时间序列中极端事件到达间隔时间的统计推断

摘要 在统计物理学研究的许多复杂系统中，太阳耀斑、交易和神经元电压等事件之间的到达间隔时间遵循重尾分布。事件时间集类似于分形，在某些时间窗口中是密集的，在其他时间窗口中是空的，这种现象被称为“突发”。提出了一种新的模型，用于高于高阈值的此类事件的相互超越时间。对于高阈值和无限平均等待时间，表明跨越阈值之间的时间是 Mittag-Leffler 分布的，因此形成了“分数泊松过程”，它概括了阈值超出的标准泊松过程。提供了估计模型参数和评估模型拟合的图形方法。推理方法应用于经验突发时间序列，