copulaCdfStudent

copulaCdfStudent(rho, nu, X)

Calculates the cumulative probability of the t copula, with linear correlation parameters rho, and degrees of freedom parameter nu evaluated at the points in X.

rho is a scalar or matrix that specifies the linear correlation parameters.

• When X is two-dimensional data, rho can be a DOUBLE scalar that specifies the correlation coefficient between the two variables. The value must be in the range (-1, 1).

• rho can also be a 2×2 correlation matrix.

nu is an INT or DOUBLE scalar that specifies the degrees-of-freedom parameter of the t copula. The value must be in the range (0, ∞).

• Smaller nu values indicate heavier tails.

• Larger nu values make the t copula approach the Gaussian copula.

X is a non-empty two-dimensional numeric matrix or table with dimensions n×p (only p = 2 is currently supported), specifying the set of evaluation points for which densities are computed. Here, n is the number of evaluation points, that is, the number of rows in X; p is the number of variables, that is, the number of columns in X.

• All elements must be finite numbers.

• Rows whose elements are all in the open interval (0, 1) are evaluated using the t copula cumulative distribution formula.

• Rows with any element u <= 0 return 0. Rows with all elements u >= 1 return 1.

• When X is a table, each column represents a variable, and the column order defines the variable order.

A DOUBLE vector with the same length as the number of rows in X. The i-th element of the returned vector is the copula cumulative probability for the i-th row of X.

Example 1. Calculate the cumulative probability of a two-dimensional t copula with correlation coefficient 0.5 at the central point [0.5, 0.5].

X = matrix([0.5], [0.5])
y = copulaCdfStudent(0.5, 5, X)
y
// Output: [0.33333333349608013]

Example 2. Evaluate multiple sets of two-dimensional pseudo-observations and demonstrate how boundary points are handled.

u1 = [0.0, 0.2, 1.0]
u2 = [0.1, 0.3, 1.0]
X = matrix(u1, u2)

y = copulaCdfStudent(0.7, 5, X)
y
// Output: [0, 0.1448277232297781, 1]

Related Functions: copulaFitStudent, copulaRandStudent, copulaPdfStudent, copulaCdfGaussian, copulaCdfClayton, copulaCdfFrank, copulaCdfGumbel