Extreme event statistics is a class of quantitative techniques focused on modeling the probability, frequency, and magnitude of rare, high-impact events using formal frameworks such as extreme value theory (EVT) and peaks-over-threshold (POT) analysis. It typically involves fitting generalized extreme value (GEV) or generalized Pareto distributions (GPD) to the tails of empirical data, estimating return levels and return periods, and quantifying tail dependence in multivariate settings. These methods are crucial in disciplines where risk is dominated by low-probability extremes, enabling rigorous extrapolation beyond observed ranges and uncertainty quantification for tail-related parameters.
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