measures.grid {GRIDCOPULA}

Returns dependency measures for a grid type copula

Description

Returns dependency measures for a grid type copula

Usage

measures.grid(gc, measures = "all")

Arguments

gc

a grid type copula object.

measures

A vector of the measurements to calculate: "gini", "blomqvist", "tail_U", "tail_L", "rho", "tau","mi", by default "all".

Details

"tau"

Kendall's \tau, see Nelsen (2007).

"rho"

Spearman's \rho, see Nelsen (2007).

"blomqvist"

Blomqvist's \beta; computed as 4C(0.5, 0.5) - 1, see Nelsen (2007).

"gini"

Gini's \gamma, see Nelsen (2007).

"mi"

Mutual information, see Joe (1989).

"tail_U/tail_L"

Tail dependency, see Nelsen (2007).

Value

A list with dependence measures

References

Nelsen, R. (2007). An introduction to copulas. Springer Science & Business Media.

Joe, H. (1989). Relative Entropy Measures of Multivariate Dependence. Journal of the American Statistical Association.

Examples

# Generating simulated data with a transformation to the copula domain
n <- 500
x <- rgamma(n,4,1/2)
e <- rnorm(n,0,.3)
y <- sin(x+e)
Fx <- ecdf(x)
Fy <- ecdf(y)
u <- Fx(x)
v <- Fy(y)
df <- cbind(u,v)
copula.grid <- estimate.gridCopula(U = df, k = 5, m = 4 , method = "ml")
measures.grid(copula.grid) 
measures.grid(copula.grid, measures = c("rho","tau","mi"))

# Using the Iris dataset, transformation is not mandatory
copula.grid <- estimate.gridCopula(X = iris[,1:2], k = 3, m = 7 , method = "ml")
measures.grid(copula.grid, measures = c("gini", "blomqvist", "tail_U", "tail_L", "rho"))