copulaRandStudent

copulaRandStudent(rho, nu, count)

Returns two-dimensional random vectors that follow a t-Copula dependence structure. Each row of the returned matrix is a two-dimensional sample, and each column follows a uniform distribution over (0, 1).

t-Copula introduces the degree-of-freedom parameter nu to the symmetric dependence structure of Gaussian Copula and can be used to simulate two-sided tail dependence. As nu increases, t-Copula approaches Gaussian Copula.

rho is a numeric scalar or a 2-by-2 numeric matrix indicating the linear correlation parameter. If it is a scalar, it specifies the two-dimensional correlation coefficient and must be in (-1, 1). If it is a matrix, it must be a positive definite correlation matrix with diagonal elements equal to 1.

nu is a positive numeric scalar indicating the degrees of freedom. In general, a smaller nu indicates stronger tail dependence. When nu is large, the result approaches Gaussian Copula.

count is a positive INT scalar indicating the number of samples to generate.

A DOUBLE matrix with count rows and 2 columns. All values are in the interval (0, 1).

setRandomSeed(seed=20260114)
u = copulaRandStudent(rho=0.5, nu=5, count=5)
shape(u)
// output: 5 :2

min(flatten(u)) > 0 && max(flatten(u)) < 1
// output: true

Specify a 2-by-2 correlation matrix for rho:

rho = [1.0, 0.5, 0.5, 1.0]$2:2
u = copulaRandStudent(rho=rho, nu=5.5, count=5)
shape(u)
// output: 5 :2

Related functions: copulaRandGaussian, copulaRandClayton, copulaRandFrank, copulaRandGumbel