Extreme Value Theory — GEV Family

The Generalized Extreme Value (GEV) distribution is the limit distribution of block maxima. Gumbel (ξ=0), Fréchet (ξ>0), Weibull (ξ<0) — all unified by the Fisher-Tippett-Gnedenko theorem.

Controls

Blocks: —
Sample mean: —
Sample std: —
GEV CDF:
G(x) = exp{−[1+ξ(x−μ)/σ]^(−1/ξ)}

ξ = 0: Gumbel (light tail)
ξ > 0: Fréchet (heavy tail)
ξ < 0: Weibull (bounded tail)

Extremes are universal —
only 3 possible limits!