← Copula mathematical handbook

Gaussian copulas

A positive semidefinite correlation matrix defines a Gaussian copula by applying the standard normal CDF to each coordinate. Singular correlation matrices are permitted: the diagonal assumption makes each marginal atomless.

theorem ProbabilityTheory.Copula.continuous_standardNormalCDF : Continuous ↑(cdf (gaussianReal 0 1))

noncomputable def ProbabilityTheory.Copula.gaussian {d : ℕ} (R : Matrix (Fin d) (Fin d) ℝ) (hR : R.PosSemidef) (hdiag : ∀ (i : Fin d), R i i = 1) : Copula d

The Gaussian copula associated to a correlation matrix.

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