copula·laboratory

simulation de structures de dépendance bivariées — théorème de Sklar

F_X,Y(x,y) = C( F_X(x), F_Y(y) )

scénarios

Copula space (U₁,U₂) ∈ [0,1]² —

1 0 U₁ → 1

—

X marginal

Y marginal

Joint distribution X = F_X⁻¹(U₁), Y = F_Y⁻¹(U₂) after marginal transform

Kendall τ

—th. —

Spearman ρ_S

—th. —

Lower tail λ_L

—th. —

Upper tail λ_U

—th. —

empirical = measured on the cloud · th. = closed-form from Cherubini–Durante–Mulinacci. Drag θ or hit animate to watch the dependence morph continuously while marginals stay fixed — that separation is Sklar's theorem.

θ—

Marginals

Rendu

la carte de densité révèle où la masse de probabilité se concentre — les coins = dépendance de queue.

Samples2000

Glow1.0×

animate sweeps θ with a tracked comet trail — points move continuously from fixed seeds (no re-sampling).