Abstract
This chapter investigates the use of Extreme Value Statistics (EVS) to probabilistically model extreme events separated as unstructured noise in signal processing. We apply a version of EVS that computes the likelihood of extreme discrepancies exceeding a selected threshold value within a given time interval. In theory, exceedances follow a Generalized Pareto (GP) distribution, and we run diagnostics to determine how well the data actually fit this distribution. If we find a reasonable fit, we can invert the GP distribution to solve for quantiles providing a useful noise diagnostic: return level plots. Return level plots show the return periods expected before particular extreme noise levels return levels are realized.
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