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- W2798521330 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. This article generalizes the Peaks Over Threshold (POT) model to the setting where inter-event times are heavy-tailed. For high thresholds and infinite-mean waiting times, we show that the times between threshold crossings are Mittag-Leffler distributed, and thus form a fractional Poisson Process which generalizes the standard Poisson Process. We provide graphical means of estimating model parameters and assessing model fit. Along the way, we apply our inference method to a real-world bursty time series, and show how the memory of the Mittag-Leffler distribution affects the predictive distribution for the time until the next extreme event." @default.
- W2798521330 created "2018-05-07" @default.
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- W2798521330 date "2018-02-14" @default.
- W2798521330 modified "2023-09-27" @default.
- W2798521330 title "Peaks Over Threshold for Bursty Time Series." @default.
- W2798521330 hasPublicationYear "2018" @default.
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