wasserstein {cylcop}

Calculate the Wasserstein Distance

Description

The Wasserstein distance is calculated based on the Euclidean distance between two copula PDFs on a grid, or between a copula PDF and pseudo-observations.

Usage

wasserstein(
  copula,
  copula2 = NULL,
  theta = NULL,
  x = NULL,
  n_grid = 2500,
  p = 2
)

Arguments

copula

R object of class 'cyl_copula'. or 'Copula' (package 'copula', only 2-dimensional).

copula2

R object of class 'cyl_copula'. or 'Copula' (package 'copula', only 2-dimensional).

theta

(alternatively) numeric vector of angles (measurements of a circular variable) or "circular" component of pseudo-observations.

x

(alternatively) numeric vector of step lengths (measurements of a linear variable) or "linear" component of pseudo-observations.

n_grid

integer number of grid cells at which the PDF of the copula(s) is calculated Default is 2500

p

integer power (1 or 2) to which the Euclidean distance between points is taken in order to compute transportation costs.

Details

Note that when comparing 2 copula PDFs (i.e. theta = NULL and x = NULL), the calculated Wasserstein distance will depend on the number of grid cells (n_grid) used to approximate the PDFs. The distance will converge to a certain value with a higher number of grid cells, but the computational time will also increase. The default of 2500 seems to be a good (empirically determined) compromise. The same is true when calculating the Wasserstein distance between a copula PDF and pseudo-observations. There, it is also important to only compare distances that use the same number of observations.

The code is based on the functions transport::wasserstein() and transport::semidiscrete().

Value

numeric, the pth Wasserstein distance

Examples

set.seed(1234)
copula1 <- cyl_quadsec(0.1)
copula2 <- cyl_rect_combine(copula::frankCopula(2))
wasserstein(copula=copula1,copula2 = copula2,p=2,n_grid=20)
wasserstein(copula=copula1,copula2 = copula1,p=2,n_grid=20)
wasserstein(copula=copula1,copula2 = copula::frankCopula(2),p=2,n_grid=20)

 sample <- rjoint(10,
  copula1,
  marginal_1 = list(name = "vonmises", coef  = list(0, 1)),
  marginal_2 = list(name = "weibull", coef = list(3,4))
)

wasserstein(copula=copula1, theta=sample[,1], x=sample[,2], n_grid=20)