zetac {depcoeff}

Zeta dependence coefficient

Description

zetac is a function to evaluate the zeta dependence coefficient (one interval) of two random variables x and y which is based on the copula. Four specific coefficients are available: the Spearman coefficient, Spearman's footrule, the power coefficient and the Huber function coefficient.

Usage

zetac(x,y,method="Spearman",methodF=1,parH=0.5,parp=1.5)

Arguments

x, y

data vectors of the two variables whose dependence is analysed.

method

list of names of the coefficients: "Spearman" stands for the Spearman coefficient, "footrule" means Spearman's footrule, "power" stands for the power function coefficient, "Huber" means the Huber function coefficient. If "all" is assigned to method then all methods are used.

methodF

value 1,2 or 3 refers to several methods for computation of the distribution function values, 1 is the default value.

parH

parameter of the Huber function (default 0.5). Valid values for parH are between 0 and 1.

parp

parameter of the power function (default 1.5). The parameter has to be positive.

Details

Let X_{1},\ldots ,X_{n} be the sample of the X variable. Formulas for the estimators of values F(X_{i}) of the distribution function: methodF = 1 \rightarrow \hat{F}(X_{i})=\frac{1}{n}\textrm{rank}(X_{i}) methodF = 2 \rightarrow \hat{F}^{1}(X_{i})=\frac{1}{n+1}\textrm{rank}(X_{i}) methodF = 3 \rightarrow \hat{F}^{2}(X_{i})=\frac{1}{\sqrt{n^{2}-1}}\textrm{rank}(X_{i}) The values of the distribution function of Y are treated analogously.

Value

zeta dependence coefficient of two random variables. This coefficient is bounded by 1. The higher the value the stronger is the dependence.

References

Eckhard Liebscher (2014). Copula-based dependence measures. Dependence Modeling 2 (2014), 49-64

Examples

library(MASS)
data<- gilgais
zetac(data[,1],data[,2])