17  Extreme Value Theory

Introduces the three limiting families for the (rescaled) maximum — Gumbel, Fréchet, Weibull — tied directly to the tail-decay taxonomy from Chapter 4: thin tails lead to Gumbel, power-law tails to Fréchet, bounded distributions to Weibull. Readers simulate maxima from all three source types and observe which limiting shape their rescaled maxima settle toward.