theta2tau, tau2theta {HAC}

Kendall's rank correlation coefficient

Description

Kendall's rank correlation coefficient and its inverse.

Usage

theta2tau(theta, type)
tau2theta(tau, type)

Arguments

theta

the dependency parameter. It can be either a scalar, a vector or a matrix and has to lie within a certain interval, 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.

tau

Kendall's rank correlation coefficient. It can be either a scalar, a vector or a matrix and it is to ensure, that \tau \in [0,1).

type

all types are available, see phi for an overview of implemented families.

Examples

# computation of the dependency parameter
x = runif(10)
theta = tau2theta(x, type = 1)

# computation of kendall's tau
y = runif(10, 1, 100)
tau = theta2tau(y, type = 1)