Dependence beyond correlation

Copula Playground

Start with the dependence shape, then move between copula ranks and observed GAMLSS margins without changing the underlying individuals.

Connecting
v0.8Exact R simulation

Dependence has shape.

Faint pseudo-observations sit underneath model-implied probability contours, making symmetry and tail concentration easier to see.

Three linked views

Inspect normal scores, the uniform copula scale, or observed values with GAMLSS marginal histograms and densities.

Interpret carefully

These are exact simulations from a chosen copula—not fitted output from an uploaded dataset.

Gaussian

Symmetric dependence

model contourssimulated peoplehighlightedtail region

Normal-score dependence

Model-implied 50%, 75%, and 90% probability contours.

fixed −3 to 3 axes
Target / simulated τ0.45 / —
Upper given upper Y1—
Lower given lower Y1—
Model tail λL / λU—
Copula parameter—
Highlighted—