= Pickands-Balkema-de Haan theorem
{c}
= Threshold excess limit theorem
{synonym}
For a distribution in an extreme-value domain of attraction, the <conditional distribution> of the excess above a high threshold is asymptotically approximated by a <generalized Pareto distribution> with a threshold-dependent scale and a limiting shape parameter. This theorem justifies the <peaks-over-threshold method>. Threshold selection must balance approximation error against the reduced number of excess observations.
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