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

 kantorovich R Documentation

Kantorovich distance

Description

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

Usage

``````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

``````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 Aug. 23, 2023, 1:06 a.m.