# kantorovich: Kantorovich distance In kantorovich: Kantorovich Distance Between Probability Measures

## Description

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

## Usage

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

## 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.

## Value

The Kantorovich distance between `mu` and `nu`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```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) ```

kantorovich documentation built on Oct. 29, 2020, 1:06 a.m.