# canberra: Canberra and related distances In kylebittinger/abdiv: Alpha and Beta Diversity Measures

## Description

The Canberra distance and Clark's coefficient of divergence are measures that use the absolute difference over the sum for each element of the vectors.

## Usage

 1 2 3 canberra(x, y) clark_coefficient_of_divergence(x, y) 

## Arguments

 x, y Numeric vectors

## Details

For vectors x and y, the Canberra distance is defined as

d(x, y) = ∑_i \frac{|x_i - y_i|}{x_i + y_i}.

Elements where x_i + y_i = 0 are not included in the sum. Relation of canberra() to other definitions:

• Equivalent to R's built-in dist() function with method = "canberra".

• Equivalent to the vegdist() function with method = "canberra", multiplied by the number of entries where x > 0, y > 0, or both.

• Equivalent to the canberra() function in scipy.spatial.distance for positive vectors. They take the absolute value of x_i and y_i in the denominator.

• Equivalent to the canberra calculator in Mothur, multiplied by the total number of species in x and y.

• Equivalent to D_{10} in Legendre & Legendre.

Clark's coefficient of divergence involves summing squares and taking a square root afterwards:

d(x, y) = √{ \frac{1}{n} ∑_i ≤ft( \frac{x_i - y_i}{x_i + y_i} \right)^2 },

where n is the number of elements where x > 0, y > 0, or both. Relation of clark_coefficient_of_divergence() to other definitions:

• Equivalent to D_11 in Legendre & Legendre.

## Value

The Canberra distance or Clark's coefficient of divergence. If every element in x and y is zero, Clark's coefficient of divergence is undefined, and we return NaN.

## Examples

 1 2 3 4 x <- c(15, 6, 4, 0, 3, 0) y <- c(10, 2, 0, 1, 1, 0) canberra(x, y) clark_coefficient_of_divergence(x, y) 

kylebittinger/abdiv documentation built on Jan. 19, 2020, 3:48 a.m.