D1 | R Documentation |
Computation of the D1 distance between two checkerboard copulas A and B, corresponding to the random vectors (X1,Y1) and (X2,Y2), respectively.
The function D1()
computes the difference between the dependence structures of two random vectors. The function D1.ECBC()
computes the D1-distance between two checkerboard copulas with the same resolution.
The function zeta1()
is defined as 3D1(A,Pi), where Pi denotes the independence copula and returns the dependence measure computed in qad.
D1(x1, y1, x2, y2, resolution = NULL) D1.ECBC(A, B) zeta1(X, Y, resolution = NULL)
x1 |
a (non-empty) numeric vector of data values for the first random vector (first coordinate) |
y1 |
a (non-empty) numeric vector of data values for the first random vector (second coordinate) |
x2 |
a (non-empty) numeric vector of data values for the second random vector (first coordinate) |
y2 |
a (non-empty) numeric vector of data values for the second random vector (second coordinate) |
resolution |
integer indicating the resolution of the checkerboard copula. (default = NULL) |
A |
Numeric matrix of dimension NxN indicating the mass of the first N-checkerboad copula |
B |
Numeric matrix of dimension NxN indicating the mass of the second N-checkerboad copula |
X |
Numeric vector of values in the first coordinate |
Y |
Numeric vector of values in the second coordinate |
D1()
returns the D1 distance, introduced in (Trutschnig, 2011).
D1.ECBC()
returns the D1-distance between to checkerboard copulas A and B with same resolution
zeta1()
returns the directed dependence from x to y.
Trutschnig, W. (2011). On a strong metric on the space of copulas and its induced dependence measure. Journal of Mathematical Analysis and Applications. 384 (2), 690-705.
Junker, R.R., Griessenberger, F. and Trutschnig, W. (2021). Estimating scale-invariant directed dependence of bivariate distributions. Computational Statistics and Data Analysis, 153, 107058.
n <- 100 x1 <- runif(n) y1 <- x1 x2 <- runif(n) y2 <- 1-x2 D1(x1,y1,x2,y2) n <- 1000 x <- runif(n, 0, 1) y1 <- ifelse(x < 0.5, runif(length(x < 0.5), 0,0.5), runif(length(x >= 0.5), 0.5, 1)) y2 <- ifelse(x > 0.5, runif(length(x < 0.5), 0,0.5), runif(length(x >= 0.5), 0.5, 1)) A <- ECBC(x,y1, resolution = 50) B <- ECBC(x,y2, resolution = 50) #plot_density(A) #plot_density(B) D1.ECBC(A,B)
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