canberra {abdiv} | R Documentation |

## Canberra and related distances

### 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

```
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) = \sum_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) = \sqrt{
\frac{1}{n} \sum_i \left( \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

```
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)
```

*abdiv*version 0.2.0 Index]