Copula Invariance Explorer

Separate a joint distribution into its margins and its dependence structure, and see which statistics survive monotone transformation.

dependence
copula
rank statistics
transformation

Pearson r (raw Y)

0.583

Pearson r (transformed)

0.583

changes

Spearman ρ (raw Y)

0.655

Spearman ρ (transformed)

0.655

invariant

Observed feature space

Copula space (ranks on the unit square)

What just happened

The right-hand panel is identical no matter which margin or transform you choose — it is the copula, the pure dependence structure. The left panel, and with it Pearson's r, is reshaped by every monotone map. Rank-based statistics read the right panel; product-moment statistics read the left.

Preparing the simulation…