Extreme Value Theory Notes
A consolidated set of notes on the foundations of extreme value theory, including block maxima, peaks over threshold, tail index interpretation, and high-quantile extrapolation.
Academic Notes · Tail Risk · Rare Events
Extreme Value Theory
Notes on rare-event modelling, block maxima, threshold exceedances, generalized extreme value limits, generalized Pareto models, tail index estimation, and extreme quantile inference.
Extreme Value Theory
Notes and drafts.
This section collects notes on the statistical modelling of rare and extreme events. The emphasis is on tail limits, threshold exceedance theory, generalized extreme value distributions, generalized Pareto models, and extreme quantile estimation.
Introduction to Extreme Value Theory
A conceptual introduction to why extremes require separate asymptotic modelling, with block maxima and threshold exceedance viewpoints.
Block Maxima and GEV Limits
A note on maxima of iid sequences, normalization, domains of attraction, and the generalized extreme value family.
Peaks Over Threshold and GPD
A note on threshold exceedances, the Pickands--Balkema--de Haan theorem, and tail modelling with the generalized Pareto distribution.
Tail Index Estimation
A note on interpreting and estimating the extreme value index, including heavy-tailed, light-tailed, and bounded-tail regimes.
Extreme Quantile Estimation
A note on estimating quantiles beyond the observed data range and why tail extrapolation requires explicit extreme-value assumptions.