Dependence beyond correlation

Copula Playground

Compare rank patterns, transformed margins, and tail co-movement. The main lesson: similar broad association can still produce very different extremes.

Connecting
v0.5 R-backed

Dependence has shape.

Align marginal densities with the joint plots, then track the same individuals through ranks and observed values.

Interpretation

View pseudo-observations on the true uniform scale or on normal-score scale, where extremes are easier to inspect.

Caveat

Simulations are package-backed in R and margins are computed with gamlss.dist; this is still an explainer, not fitted model output.

Gaussian

Same association, different extremes

rank pairs aligned margins individuals highlighted tail zone

Pseudo-Observations

Observed Values

Upper co-movement 0%
Lower co-movement 0%
Rank correlation 0
Margins -
Highlighted -