kantorovich (version 3.1.0)

kantorovich: Kantorovich distance

Description

Compute the Kantorovich distance between two probability measures on a finite set.

Usage

kantorovich(mu, nu, dist = NULL, details = FALSE, ...)

Value

The Kantorovich distance between mu and nu.

Arguments

mu

(row margins) probability measure in numeric or bigq/character mode

nu

(column margins) probability measure in numeric or bigq/character mode

dist

function or matrix, the distance to be minimized on average; if NULL, the 0-1 distance is used.

details

prints the joinings achieving the Kantorovich distance and returns them in the "joinings" attribute of the output

...

arguments passed to dist (only if it is a function)

Details

The function firstly computes all the extreme joinings of mu and nu, then evaluates the average distance for each of them, and then returns the minimal one.

Examples

mu <- c(1/7, 2/7, 4/7)
nu <- c(1/4, 1/4, 1/2)
kantorovich(mu, nu)
library(gmp)
mu <- as.bigq(c(1,2,4), 7)
nu <- as.bigq(c(1,1,1), c(4,4,2))
kantorovich(mu, nu)
mu <- c("1/7", "2/7", "4/7")
nu <- c("1/4", "1/4", "1/2")
kantorovich(mu, nu, details=TRUE)