phi function

Generator function

The Archimedean generator function and its inverse.

phi(x, theta, type)
phi.inv(x, theta, type)

Arguments

• x: a scalar, vector or matrix at which the function is evaluated. The support of the functions has to be taken into account, i.e. $x \in [0, \infty]$ for the generator function and $x \in [0, 1]$ for its inverse.

• theta: the feasible copula parameter, i.e. $\theta \in [1, \infty)$ for the Gumbel and Joe family, $\theta \in (0, \infty)$ for the Clayton and Frank family and $\theta \in [0, 1)$ for the Ali-Mikhail-Haq family.

• type: select between the following integer numbers for specifying the type of the hierarchical Archimedean copula (HAC) or Archimedean copula (AC):

  • 1 = HAC Gumbel
  • 2 = AC Gumbel
  • 3 = HAC Clayton
  • 4 = AC Clayton
  • 5 = HAC Frank
  • 6 = AC Frank
  • 7 = HAC Joe
  • 8 = AC Joe
  • 9 = HAC Ali-Mikhail-Haq
  • 10 = AC Ali-Mikhail-Haq

Examples

x = runif(100, min = 0, max = 100)
phi(x, theta = 1.2, type = 1)

# do not run
# phi(x, theta = 0.8, type = 1) 
# In phi(x, theta = 0.8, type = 1) : theta >= 1 is required.