Copula name

Gaussian copula

Common notation

Parameters

, a non-negative definite  matrix, i.e. a matrix that can correspond to a correlation matrix

Domain

Copula

where  is the inverse normal function and  is the cumulative distribution function of the multivariate normal distribution defined by a covariance matrix equal to

Kendall’s rank correlation coefficient (for bivariate case),

Where  is the correlation coefficient between the two variables

Coefficient of upper tail dependence,

 (unless the correlation matrix exhibits perfect positive or negative dependence)

Coefficient of lower tail dependence,

 (unless the correlation matrix exhibits perfect positive or negative dependence)

Other comments

The Spearman rank correlation coefficient is given by:

where  is the (normal) correlation coefficient between the two variables.

If  (the  identity matrix) then we obtain the independence copula.