phi: Generator function

In HAC: Estimation, Simulation and Visualization of Hierarchical Archimedean Copulae (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.

HAC documentation built on Sept. 17, 2024, 1:06 a.m.