mixle.utils.automatic.detectors.generalized_pareto module

Generalized Pareto (peaks-over-threshold) continuous candidate – heavy-tailed exceedances.

By the Pickands-Balkema-de Haan theorem the distribution of exceedances over a high threshold converges to a generalized Pareto distribution (GPD). Its signature is a strictly-positive, monotone-decreasing density with a heavy (Pareto) upper tail – shape xi clearly above 0.

The xi -> 0 limit of the GPD is the exponential, and the gamma family already covers that (and the exponential itself); to avoid stealing exponential / gamma data the gate fires only when a moment estimate of the tail index xi is unmistakably positive (a genuinely heavy tail). With that gate, exponential and Gaussian data never reach this candidate.