Let , and let
be a univariate t distribution with
degrees of freedom.
The Student’s t copula can be written as
where is the multivariate Student’s t distribution that has a correlation matrix
with
degrees of freedom.
The input parameters for the simulation are . The
copula can be simulated by the following steps:
Generate a multivariate vector that follows the centered t distribution with
degrees of freedom and correlation matrix
.
Transform the vector into
, where
is the distribution function of univariate t distribution with
degrees of freedom.
To simulate centered multivariate t random variables, you can use the property that if
, where
and the univariate random variable
.