Demonstrate, by direct integration, that the factor copula: is itself equivalent to an n-dimensional Gaussian copula with correlation matrix ij = ij . Show further

Demonstrate, by direct integration, that the factor copula:

is itself equivalent to an n-dimensional Gaussian copula with correlation matrix ρij = λiλj . Show further that the corresponding correlation matrix for the factor copula:

is positive semi-definite ∀ |λi| ≤ 1.

C(u1,..., un) = = /* II -AV +(u1) (V)dV i=1,n 1-X2