frechet (version 0.3.0)

dist4den: \(L^2\) Wasserstein distance between two distributions.

Description

\(L^2\) Wasserstein distance between two distributions.

Usage

dist4den(d1 = NULL, d2 = NULL, fctn_type = NULL, optns = list())

Value

A scalar holding the \(L^2\) Wasserstein distance between d1 and d2.

Arguments

d1, d2

Lists holding the density functions or quantile functions of the two distributions. Each list consists of two numeric vectors x and y of the same length, where x holds the support grid and y holds the values of the function. Note that the type of functions representing the distributions in d1 and d2 should be the same---either both are density functions, or both are quantile functions. If both are quantile functions, all elements in d1$x and d2$x must be between 0 and 1. d1$x and d2$x may have different lengths.

fctn_type

Character vector of length 1 holding the function type in d1 and d2 representing the distributions: "density" (default), "quantile".

optns

A list of control parameters specified by list(name=value).

Details

Available control options are:

nqSup

A scalar giving the length of the support grid of quantile functions based on which the \(L^2\) Wasserstein distance (i.e., the \(L^2\) distance between the quantile functions) is computed. Default is 201.

Examples

d1 <- list(x = seq(-6,6,0.01))
d1$y <- dnorm(d1$x)
d2 <- list(x = d1$x + 1)
d2$y <- dnorm(d2$x, mean = 1)
dist <- dist4den(d1 = d1,d2 = d2)