An Introduction to Statistical Modeling of Extreme Values¶
Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Mechanisms¶
- Empirical Distribution and Increment Fit
- It cannot extrapolate beyond the observed range — the empirical tail simply stops at the sample maximum, which is exactly where rare-event questions live — and it is data-hungry precisely there.
This sourceExplains that an empirical distribution cannot extrapolate beyond the observed range because its tail ends at the sample maximum.
- It cannot extrapolate beyond the observed range — the empirical tail simply stops at the sample maximum, which is exactly where rare-event questions live — and it is data-hungry precisely there.
- Rare-Event Stress Simulation
- Its gravest failure is extrapolating the body into the tail: a distribution fit to everyday data may say a catastrophe is essentially impossible precisely because no catastrophe was in the fitting sample, and the simulation faithfully reproduces that false comfort.
This sourceShows why tail risk needs extreme-value methods and cautious extrapolation rather than an ordinary-data fit carried into the tail.
- Its gravest failure is extrapolating the body into the tail: a distribution fit to everyday data may say a catastrophe is essentially impossible precisely because no catastrophe was in the fitting sample, and the simulation faithfully reproduces that false comfort.
- Tail and Boundary Stress Scenario
- Plausible tail extrapolation is anchored by extreme value theory, which describes the limiting behavior of maxima and threshold exceedances and lets a stress be expressed as a defensible return period rather than an arbitrary shock.
This sourceUses extreme-value models for maxima and threshold exceedances to extrapolate rare events and express stresses through return levels and return periods.
- Plausible tail extrapolation is anchored by extreme value theory, which describes the limiting behavior of maxima and threshold exceedances and lets a stress be expressed as a defensible return period rather than an arbitrary shock.
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