Supplementary material to "Characterizing Climate-Driven Shifts in Chilean Rainfall Regimes with a Hybrid Hidden Markov–Copula Framework"

u] should be approximately linear.Its slope diagnoses the shape parameter ξ: flat 190 ⇒ ξ ≈ 0 (Exponential-like), increasing ⇒ ξ > 0 (heavy/unbounded tail), decreasing 191 ⇒ ξ < 0 (bounded tail).Dashed vertical lines mark u * .Qualitative reading by state 192 is provided in the main text and recapped here: State 0 ξ ≈ 0; States 1-2 ξ > 0; 193 States 3-4 ξ < 0. 194 S5 Vine-copula selection and goodness-of-fit 195 Expanded diagnostics for the dependence layer (see main §??).