phi, phi.inv {HAC}

Generator function

Description

The Archimedean generator function and its inverse.

Usage

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.