Extreme-value classification
Section of A first look at extremes, part of Stochastic processes
Extreme-value classification
| Type | Section |
| Taught in | A first look at extremes |
| Part | Stochastic processes |
Any non-degenerate limit of an affinely normalised maximum of independent copies, when such a limit exists, belongs to one of these three types. The classification does not say that every distribution has such a limit. It does not identify the tail from a short sample. Dependence, a distribution that changes with time, a measurement ceiling, and the choice of threshold can all dominate the numerical approximation. The calculations above are the exact limits for three specific laws. They are not an estimation procedure for a tail index.
Used in
See also
Exponential tails, and the Gumbel law · Power-law tails, and the Fréchet law · A finite endpoint, and a Weibull extreme-value law · Pareto distribution