copulaRandFrank

copulaRandFrank(alpha, count)

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

Frank Copula is used to simulate symmetric dependence without clear tail dependence. A positive alpha indicates positive dependence, and a negative alpha indicates negative dependence.

alpha is a numeric scalar indicating the shape parameter. alpha = 0 indicates independence. A larger absolute value of alpha indicates stronger dependence.

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).

Generate positively dependent samples with a positive alpha:

setRandomSeed(seed=20260114)
positiveU = copulaRandFrank(alpha=5.0, count=5)
shape(positiveU)
// output: 5 :2

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

Generate negatively dependent samples with a negative alpha:

setRandomSeed(seed=20260114)
negativeU = copulaRandFrank(alpha=-3.0, count=5)
shape(negativeU)
// output: 5 :2

Related functions: copulaRandGaussian, copulaRandStudent, copulaRandClayton, copulaRandGumbel