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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