Extreme Value Statistics

Controls

Distribution Type Gumbel (Type I) Fréchet (Type II) Weibull (Type III) Sample size N: 500 Block size m: 50 Shape ξ (Fréchet/Weibull): 0.50 Generate New Sample

Extreme Value Theory (EVT) states that block maxima converge to the Generalized Extreme Value (GEV) distribution. Gumbel (ξ=0) for exponential tails, Fréchet (ξ>0) for heavy tails, Weibull (ξ<0) for bounded distributions. Return levels indicate thresholds exceeded on average once every T events.